Methods for suppressing nonlinear oscillations in astatic auto-piloted aircraft control systems

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes, 4th ed. (Nauka, Moscow, 1983) [in Russian].

V. G. Boltyanskii, Mathematical Method of Optimal Control (Nauka, Moscow, 1969) [in Russian].

V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control (Nauka, Moscow, 1979) [in Russian].

A. M. Formal’skii, Controlability and Stability of Systems with Limited Resources (Nauka, Moscow, 1974) [in Russian].

F. L. Chernous’ko, I. M. Anan’evskii, and S. A. Reshmin, Control Methods of Nonlinear Mechanical Systems (Fizmatlit, Moscow, 2006) [in Russian].

A. M. Formalskii, Stabilization and Motion Control of Unstable Objects (Moscow, Fizmatlit, 2012; Walter de Grüter, Berlin, Boston, 2015).

S. Tarbouriech, G. Garcia, J. Gomes da Silva, Jr., and I. Queinnec, Stability and Stabilization of Linear Systems with Saturating Actuators (Springer, London, 2011).

V. N. Bukov, Adaptive Predictive Flight Control Systems (Nauka, Moscow, 1987) [in Russian].

G. S. Byushgens and R. V. Studnev, Aerodynamics of an Aircraft: Dynamics of Longitudinal and Lateral Motion (Moscow, Mashinostroenie, 1979), p. 352 [in Russian].

V. S. Berko, Yu. G. Zhivov, and A. M. Poedinok, “Approximate criteria of forced vibration stability of regulated objects with nonlinear actuator,” Uch. Zap. TsAGI 25 (4), 72–80 (1984).

Aviation Safety and Pilot Control: Understanding and Preventing Unfavorable Pilot-Vehicle Interactions, Ed. by D. T. McRuer and J. D. Warner (Committee on the Effects of Aircraft-Pilot Coupling on Flight Safety Aeronautics and Space Engineering Board Commission on Engineering and Technical Systems National Research Council National Academy Press, Washington, DC, 1997).

O. Brieger, M. Kerr, D. Leißling, et al., “Anti-windup compensation of rate saturation in an experimental aircraft,” in Proceedings of the American Control Conference ACC 2007 (IEEE, New York, 2007), pp. 924–929.

O. Brieger, M. Kerr, J. Postlethwaite, et al., “Flight testing of low-order anti-windup compensators for improved handling and PIO suppression,” in Proceedings of the American Control Conference ACC 2008 (AACC, Seattle, USA, 2008), pp. 1776–1781.

O. Brieger, M. Kerr, D. Leißling, et al., “Flight testing of a rate saturation compensation scheme on the ATTAS aircraft,” Aerospace Sci. Technol. 13, 92–104 (2009).

O. Brieger, M. Kerr, I. Postlethwaite, et al., “Pilot-involved-oscillation suppression using low-order antiwindup: flight-test evaluation,” J. Guidance, Control, Dyn. 35, 471–483 (2012).

B. Powers, “Space shuttle pilot-induced-oscillation research testing,” NASA Technical Memorandum No. 86034 (NASA Am. Res. Center, Dryden Flight Research Facility, Edwards, California, USA, 1984).

Aerodynamics, Stability and Controllability of Supersonic Aircrafts, Ed. by G. S. Byushgens (Nauka, Fizmatlit, Moscow, 1998), p. 816 [in Russian].

M. Pachter and R. Miller, “Manual flight control with saturating actuators,” IEEE Control Syst. Mag. 18, 10–19 (1998).

D. Acosta, M. Y. Yildiz, and D. H. Klyde, “Avoiding pilot-induced oscillations in energy-efficient aircraft designs,” in The Impact of Control Technology, 2nd ed., Ed. by T. Samad and A. Annaswamy (IEEE Control Systems Society, 2014).

H. Duda, “Flight control system design considering rate saturation,” Aerospace Sci. Technol. 4, 265–215 (1998).

B. V. Raushenbakh and E. N. Tokar’, Orientation Control of Spacecrafts (Nauka, Moscow, 1974) [in Russian].

L. I. Kargu, Systems of Angular Stabilisation of Spacecrafts, 2nd ed. (Mashinostroenie, Moscow, 1980) [in Russian].

V. O. Bragin, V. I. Vagaitsev, N. V. Kuznetsov, and G. A. Leonov, “Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits,” J. Comput. Syst. Sci. Int. 50, 511 (2011).

G. Leonov and N. Kuznetsov, “Hidden attractors in dynamical systems: from hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits,” Int. J. Bifurcat. Chaos 23, Art. num. 1330002 (2013).

N. Kuznetsov and G. Leonov, “Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors [survey paper],” in Proceedings of the 19th International Federation of Automatic Control IFAC World Congress, Cape Town, South Africa, IFAC Proc. Vols. (IFAC-PapersOnline), Vol. 47, 5445–5454 (2014).

B. Andrievsky, N. Kuznetsov, G. Leonov, and S. Seledzhi, “Hidden oscillations in stabilization system of flexible launcher with saturating actuators,” in Proceedings of the 19th IFAC Symposium on Automatic Control in Aerospace ACA 2013, Wurzburg, Germany, IFAC Proc. Vols. (IFAC-PapersOnline), Vol. 19, 37–41 (2013).

B. Andrievsky, N. Kuznetsov, G. Leonov, and A. Pogromsky, “Hidden oscillations in aircraft flight control system with input saturation,” in Proceedings of the 5th IFAC International Workshop on Periodic Control Systems PSYCO 2013, Caen, France, IFAC Proc. Vols. (IFAC-PapersOnline), Vol. 5, 75–79 (2013).

A. V. Efremov and A. A. Korovin, “Modification of the criteria for piloting characteristics assessing and the phenomenon of aircraft pumping by pilot,” Tr. MAI., No. 55, 1–12 (2012).

A. V. Efremov, A. A. Korovin, and A. V. Koshelenko, “Technique for flying qualities and PIO prediction,” in Proceedings of the 28th Congress of the International Council of the Aeronautical Sciences, ICAS 2012, Brisbane, Australia, Ed. by I. Grant (ICAS, 2012), p. ICAS 2012-5.9.2.

A. V. Efremov and A. V. Ogloblin, “Progress in pilot-in the loop investigations for flying qualities prediction and evaluation,” in Proceedings of the 25th International Congress of Aeronautical Sciences, ICAS 2006, Hamburg, Germany, Ed. by I. Grant (ICAS, 2006), p. ICAS 2006-6.9.1.

A. V. Efremov, A. V. Ogloblin, A. N. Predtechenskii, and V. V. Rodchenko, The Pilot as a Dynamical System (Mashinostroenie, Moscow, 1992) [in Russian].

J. C. Lozier, “A steady-state approach to the theory of saturable servo systems,” IRE Trans. Automat. Contr. 1, 19–39 (1956).

K. Åström and B. Wittenmark, Computer-Controlled Systems. Theory and Design (Prentice Hall, Upper Saddle River, NJ, 1997; Mir, Moscow, 1987).

P. Hippe and C. Wurmthaler, “Systematic closed-loop design in the presence of input saturation,” Automatica 35, 689–695 (1999).

G. A. Leonov, B. R. Andrievskii, N. V. Kuznetsov, and A. Yu. Pogromskii, “Aircraft control with anti-windup compensation,” Differ. Uravn. Processy Upravl., No. 3 (2012).

G. Leonov, B. Andrievskii, N. Kuznetsov, and A. Pogromskii, “Aircraft control with anti-windup compensation,” Differ. Equations 48, 1700–1720 (2012).

M. Kothare, P. Campo, M. Morari, and C. Nett, “A unified framework for the study of antiwindup designs,” Automatica 30, 1869–1883 (1994).

R. Hanus, M. Kinnaert, and J.-L. Henrotte, “Conditioning technique, a general anti-windup and bumpless transfer method,” Automatica 23, 729–739 (1987).

E. Mulder, M. Kothare, and M. Morari, “Multivariable anti-windup controller synthesis using linear matrix inequalities,” Automatica 37, 1407–1416 (2001).

K. Åström and J. L. Rundqwist, “Integrator windup and how to avoid it,” in Proceedings of the American Control Conference ACC'89, Pittsburgh, PA, USA, 1989, Vol. 2, pp. 1693–1698.

S. Tarbouriech and M. Turner, “Anti-windup design: an overview of some recent advances and open problems,” IET Control Theory Appl. 3, 1–19 (2009).

Y. Peng, D. Vrancic, and R. Hanus, “Anti-windup, bumpless, and conditioned transfer techniques for PID controllers,” Control Syst. Mag. 16 (4), 48–57 (1996).

D. Bernstein and A. Michel, “A chronological bibliography on saturating actuators,” Int. J. Robust Nonlin. Control. 5, 375–380 (1995).

A. Glattfelder and W. Schaufelberger, Control Systems with Input and Output Constraints (Springer, Berlin, Heidelberg, 2003).

P. Hippe, Windup in Control: Its Effects and Their Prevention (Springer, New York, 2006).

S. Galeani, S. Tarbouriech, M. Turner, and L. Zaccarian, “A tutorial on modern anti-windup design,” in Proceedings of the 10th European Control Conference ECC 2009, Budapest, Hungary, 2009, pp. 306–323.

L. Zaccarian and A. Teel, Modern Anti-Windup Synthesis: Control Augmentation for Actuator Saturation (Princeton Univ. Press, Princeton, 2011).

R. Hanus, “Antiwindup and bumpless transfer: a survey,” in Proceedings of the 12th International Association for Mathematics and Computers in Simulation IMACS World Congress, Paris, France, July 18–22, 1988, Vol. 2, pp. 59–65.

A. Glattfelder and W. Scaufelberger, “Stability analysis of single loop control systems with saturation and antireset-windup circuits,” IEEE Trans. Autom. Control 28, 1074–1081 (1983).

R. Hanus, “A new technique for preventing control windup,” Journal A 21, 15–20 (1980).

G. Zames, “On the input-output stability of time-varying nonlinear feedback systems. Part II: Conditions involving circles in the frequency plane and sector nonlinearities,” IEEE Trans. Autom. Control 11, 465–476 (1966).

A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, The Stability of Nonlinear Systems with a Nonunique Equilibrium State (Nauka, Moscow, 1978) [in Russian].

J. Hsu and A. Meyer, Modern Control Principles and Applications (McGraw-Hill, New York, 1968; Mashinostroenie, Moscow, 1972).

A. Glattfelder and W. Schaufelberger, “Stability of discrete override and cascade-limiter single-loop control systems,” IEEE Trans. Autom. Control 33, 532–540 (1988).

E. Jury and B. Lee, “On the stability of a certain class of nonlinear sampled data systems,” IEEE Trans. Autom. Control 9, 51–61 (1964).

Ya. Z. Tsypkin, “Frequency criteria for absolute stability of nonlinear sampled-data systems,” Avtom. Telemekh., No. 3, 281–289 (1964).

P. Kapasouris and M. Athans, “Multivariable control systems with saturating actuators antireset windup strategies,” in Proceedings of the American Control Conference ACC’85, Boston, MA, USA, 1985, pp. 1579–1584.

M. Safonov and M. Athans, “A multiloop generalization of the circle criterion for stability margin analysis,” IEEE Trans. Autom. Control. 26, 415–422 (1981).

J. Doyle and G. Stein, “Multivariable feedback design: concepts for a classical/modern synthesis,” IEEE Trans. Autom. Control. 26, 4–16 (1981).

P. Kapasouris, M. Athans, and G. Stein, “Design of feedback control systems for stable plants with saturating actuators,” in Proceedings of the 27th IEEE Conference on Decision and Control CDC88, Austin, Texas, 1988 (IEEE, 1988), Vol. 1, pp. 469–479.

P. Kapasouris and M. Athans, “Control Systems with Rate and Magnitude Saturation for Neutrally Stable Open Loop Systems,” in Proceedings of the 29th IEEE Conference on Decision and Control CDC’90, Honolulu, Hawaii (IEEE, 1990), Vol. 6, pp. 3404–3409.

P. Chandler, M. Mears, and M. Pachter, “Online optimizing networks for reconfigurable control,” in Proceedings of the 32nd IEEE Conference Decision and Control CDC'1993, San Antonio, TX (IEEE, Piscataway, NJ, 1993), Vol. 3, pp. 2272–2275.

J. Hopfield and D. Tank, “'Neural' computation of decisions in optimization problems,” Biol. Cybernet. 52, 141–152 (1985).

P. Chandler, M. Mears, and M. Pachter, “A hybrid LQR/LP approach for addressing actuator saturation in feedback control,” in Proceedings of the 33rd IEEE Conference Decision and Control CDC'1994, Lake Buena Vita, FL (IEEE, Piscataway, NJ, 1994), Vol. 4, pp. 3860–3867.

H. Michalska and D. Mayne, “Robust receding horizon control of constrained nonlinear systems,” IEEE Trans. Autom. Control 28, 1623–1633 (1993).

M. Kothare and M. Morari, “Multiplier theory for stability analysis of anti-windup control systems,” Automatica 35, 917–928 (1999).

Ch. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Classics in Applied Mathematics (Academic, New York, 1975; Nauka, Moscow, 1983).

V. Balakrishnan, “Linear matrix inequalities in robustness analysis with multipliers,” Systems Control Lett. 25, 265–272 (1995).

G. Zames and P. Falb, “Stability conditions for systems with monotone and slope-restricted nonlinearities,” J. SIAM 6, 89–108 (1968).

S. Boyd, L. Ghaoui, E. E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Vol. 15: Studies in Applied Mathematics (Soc. Ind. Appl. Math. SIAM, Philadelphia, USA, 1994).

A. N. Churilov and A. V. Gessen, Study of Linear Matrix Inequalities. The Guide to Software Packages (St. Pb. Gos. Univ., St. Petersburg, 2004) [in Russian].

M. Kothare and M. Morari, “Multivariable antiwindup controller synthesis using multi-objective optimization,” in Proceedings of the American Control Conference ACC'97, Albuquerque, NM, USA, 1997, Vol. 5, pp. 3093–3097.

G. Grimm, J. Hatfield, I. Postlethwaite, et al., “Antiwindup for stable linear systems with input saturation: an LMI-based synthesis,” IEEE Trans. Autom. Control 48, 1509–1524 (2003).

Kh. K. Khalil, Nonlinear Systems (Inst. Komp’yut. Issled., Izhevsk, 2009) [in Russian].

V. Marcopoli and R. S. M. Phillips, “Analysis and synthesis tools for a class of actuator-limited multivariable control systems: a linear matrix inequality approach,” Int. J. Robust Nonlin. Control. 6, 1045–1063 (1996).

C. Barbu, R. Reginatto, A. R. Teel, and L. Zaccarian, “Anti-windup design for manual flight control,” in Proceedings of the American Control Conference ACC’99, San Diego (AACC, 1999), Vol. 5, pp. 3186–3190.

A. Teel and N. Kapoor, “The anti-windup problem: its definition and solution,” in Proceedings of the 4th European Control Conference, Brussels, Belgium, 1997.

L. Zaccarian and A. Teel, “Nonlinear scheduled anti-windup design for linear systems,” IEEE Trans. Autom. Control 49, 2055–2061 (2004).

F. Wu and M. Soto, “Extended LTI anti-windup control with actuator magnitude and rate saturations,” in Proceedings of the 42nd IEEE Conference on Decision and Control CDC 2003, Maui, Hawaii, USA (IEEE, 2003), Vol. 3, pp. 2786–2791.

F. Wu and M. Soto, “Extended anti-windup control schemes for LTI and LFT systems with actuator saturations,” Int. J. Robust Nonlin. Control 14, 1255–1281 (2004).

S. Galeani, S. Onori, A. R. Teel, and L. Zaccarian, “A magnitude and rate saturation model and its use in the solution of a static anti-windup problem,” Syst. Control Lett. 57, 1–9 (2008).

A. Teel and J. Buffington, “Anti-windup for an F-16’s daisy chain control allocator,” in Proceedings of the AIAA GNC Conference, New Orleans, LA, USA, 1997, pp. 748–754.

C. Barbu, R. Reginatto, A. Teel, and L. Zaccarian, “Anti-windup for exponentially unstable linear systems with inputs limited in magnitude and rate,” in Proceedings of the American Control Conference ACC 2000, Chicago, IL, USA, 2000, pp. 1230–1234.

N. Wada and M. Saeki, “Synthesis of a static anti-windup compensator for systems with magnitude and rate limited actuators,” in Proceedings of the 3rd IFAC Symposium on Robust Control Design ROCOND’2000, Prague, Czech Republic (IFAC, 2000), pp. 131–136.

A. Saberi, A. Stoorvogel, and P. Sannuti, Control of Linear Systems with Regulation and Input Constraints (Springer, London, 2000).

T. Hu, Z. Lin, and B. Chen, “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica 38, 351–359 (2002).

G. Ferreres and J. Biannic, “Convex design of a robust antiwindup controller for an LFT model,” IEEE Trans. Autom. Control 52, 2173–2177 (2007).

R. Reichert, “Dynamic scheduling of modern robust control autopilot design for missiles,” IEEE Control Syst. Mag. 12 (5), 35–42 (1992).

I. Queinnec, S. Tarbouriech, and G. Garcia, “Anti-windup design for aircraft flight control,” in Proceedings of the IEEE International Symposium on Intelligent Control, Münich, Germany, 2006, pp. 2541–2546.

C. Roos and J. Biannic, “Aircraft-on-ground lateral control by an adaptive LFT-based anti-windup approach,” in Proceedings of the IEEE International Symposium on Intelligent Control, Münich, Germany, 2006, pp. 2207–2212.

P. Tiwari, E. Mulder, and M. Kothare, “Multivariable anti-windup controller synthesis incorporating multiple convex constraints,” in Proceedings of the American Control Conference ACC 2007, New York, USA (IEEE, 2007), pp. 5212–5217.

N. E. Kahveci, P. A. Ioannou, and M. D. Mirmirani, “A robust adaptive control design for gliders subject to actuator saturation nonlinearities,” in Proceedings of the American Control Conference ACC 2007, New York, USA (IEEE, 2007), pp. 492–497.

N. E. Kahveci, P. A. Ioannou, and M. D. Mirmirani, “Adaptive LQ control with anti-windup augmentation to optimize UAV performance in autonomous soaring applications,” IEEE Trans. Control. Syst. Technol. 16, 691–707 (2008).

G. Herrmann, M. C. Turner, and I. Postlethwaite, “Discrete-time and sampled-data anti-windup synthesis: stability and performance,” Int. J. Syst. Sci. 37, 91–113 (2006).

J.-S. Yee, J. L. Wang, and N. Sundararajan, “Robust sampled data-flight controller design for high stabilityaxis roll manoeuver,” Control Eng. Practice 8, 735–747 (2001).

J. Biannic, S. Tarbouriech, and D. Farret, “A practical approach to performance analysis of saturated systems with application to fighter aircraft flight controllers,” in Proceedings of the 5th IFAC Symposium ROCOND, Toulouse, France, 2006, IFAC Proc. Vols. (IFAC-PapersOnline) 39, 35–40 (2006).

J. Biannic and S. Tarbouriech, “Stability and performance enhancement of a fighter aircraft flight control system by a new anti-windup approach,” in Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace ACA 2007, Toulouse, France, IFAC Proc. Vols. (IFAC-PapersOnline) 17, 177–182 (2007).

J. Biannic and S. Tarbouriech, “Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems,” Control Eng. Practice 17, 703–713 (2009).

J. Biannic, C. Roos, and S. Tarbouriech, “A practical method for fixed-order anti-windup design,” in Proceedings of the IFAC Symposium on Nonlinear Control Systems NOLCOS'2007, Pretoria, IFAC Proc. Vol. (IFAC-PapersOnline) 40, 675–680 (2007).

C. Roos and J. Biannic, “A convex characterization of dynamically-constrained anti-windup controllers,” Automatica 44, 2449–2452 (2008).

G. L. Grodzovskii, Yu. N. Ivanov, and V. V. Tokarev, Mechanics of Low Thrust Space Flight (Fizmatgiz, Moscow, 1966) [in Russian].

Theoretical Principles of Designing Information Control Systems for Space Vehicles, Ed. by E. A. Mikrin (Nauka, Moscow, 2006) [in Russian].

N. E. Zubov, “Algorithmic implementation of an automatic regime for orbital orientation of a spacecraft,” Sov. J. Comp. Syst. Sci. 28, 143–151 (1990).

E. A. Mikrin, N. E. Zubov, S. S. Negodyaev, and A. V. Bogachev, “Optimal control of spacecraft orbital orientation based on the algorithm with a predictive model,” Tr. MFTI 2 (3), 189–195 (2010).

N. E. Zubov, E. A. Mikrin, S. S. Negodyaev, and I. N. Lavrent’ev, “Spacecraft approach control synthesis with the polar scheme of a propulsion device by the free trajectory method based on the optimal control algorithm with a predictive model,” Tr. MFTI 2 (3), 168–173 (2010).

E. A. Mikrin, M. V. Mikhailov, and S. N. Rozhkov, “Autonomous navigation and rendezvous of spacecraft in lunar orbit,” Gyrosc. Navigat. 1, 310–320 (2010).

C. Pittet, N. Despre, S. Tarbouriech, and C. Prieur, “Nonlinear controller design for satellite reaction wheels unloading using anti-windup techniques,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibition, Honolulu, USA, 2008.

J. Boada, C. Prieur, S. Tarbouriech, et al., “Anti-windup design for satellite control with microthrusters,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibition, Chicago, USA, 2009.

J. Boada, “Satellite control with saturating inputs,” PhD (Math.) Thesis (ISAE, 2010).

J. Boada, C. Prieur, S. Tarbouriech, et al., “Multi-saturation anti-windup structure for satellite control,” in Proceedings of the 2010 American Control Conference ACC 2010, Baltimore, USA, 2010, pp. 5979–5984.

J. Boada, C. Prieur, S. Tarbouriech, et al., “Extended model recovery anti-windup for satellite control,” in Proceedings of the 18th IFAC Symposium on Automatic Control in Aerospace ACA 2010, Nara-ken Shinkokaido, Japan, Ed. by Y. Ochi, H. Siguerdidjane, and S. Nakasuk, IFAC Proc. Vol. (IFAC-PapersOnline), Vol. 43 (15), 205–210 (2010).

J. Boada, C. Prieur, S. Tarbouriech, et al., “Formation flying control for satellites: anti-windup based approach,” in Modeling and Optimization in Space Engineering, Vol. 73 of Springer Series Optimization and Its Applications, Ed. by G. Fasano and J. D. Pinter (Springer, London, 2013), pp. 61–83.

A. V. Bogachev, E. A. Vorob’eva, N. E. Zubov, E. A. Mikrin, M. Sh. Misrikhanov, V. N. Ryabchenko, and S. N. Timakov, “Unloading angular momentum for inertial actuators of a spacecraft in the pitch channel,” J. Comput. Syst. Sci. Int. 50, 483 (2011).

N. Zubov, E. E. Mikrin, A. S. Negodyaev, S. V. Ryabchenko, N. A. Bogachev, and E. A. Vorob’eva, “Synthesis of the three-channel system unloading kinetic momentum of inertia actuators in a spacecraft in a circular orbit,” Tr. MFTI 5 (4), 18–25 (2013).

D. Lagoutte, J. Brochot, D. de Carvalho, et al., “The DEMETER science mission centre,” Planet. Space Sci. 54, 428–440 (2006).

S. Janson, H. Helvajian, S. Amimoto, et al., “Microtechnology for space systems,” in Proceedings of the IEEE Aerospace Conference, Snowmass at Aspen, CO, USA, March 21–28, 1998 (IEEE, 1998), Vol. 1, pp. 409–418.

S. W. Janson, H. Helvajian, and K. Breuer, “MEMS, microengineering and aerospace systems,” in Proceedings of the 30th AIAA Fluid Dynamics Conference, Norfolk, VA, USA (AIAA, 1999), p. 99–3802.

A. Teel and N. Kapoor, “Uniting local and global controllers,” in Proceedings of the 4th European Control Conference ECC’97, Brussels, Belgium, 1997.

J. M. G. da Silva,Jr. and S. Tarbouriech, “Antiwindup design with guaranteed regions of stability: an LMI-based approach,” IEEE Trans. Autom. Control 50, 106–111 (2005).

B. P. Demidovich, Lectures on Mathematical Theory of Stability, The School-Book for Higher School (Nauka, Fizmatlit, Moscow, 1967) [in Russian].

A. Pogromsky and R. van den Berg, “Frequency domain performance analysis of Lur’e systems,” IEEE Trans. Contr. Syst. Technol. 22, 1949–1955 (2014).

R. van den Berg, A. Y. Pogromsky, G. A. Leonov, and J. E. Rooda, “Design of convergent switched systems,” in Group Coordination and Cooperative Control, Vol. 336: Lecture Notes in Control and Information Sciences, Ed. by K. Y. Pettersen and J. Y. Gravdahl (Springer, Berlin, 2006), pp. 291–311.

W. van den Bremer, R. van den Berg, A. Pogromsky, and J. Rooda, “An anti-windup based approach to the control of manufacturing systems,” in Proceedings of the 17th IFAC World Congress, Seoul, Korea, IFAC Proc. Vol. (IFAC-PapersOnline), Vol. 41, No. 2, 8351–8356 (2008).

A. Pogromsky, B. Andrievsky, and J. Rooda, “Aircraft flight control with convergence-based anti-windup strategy,” in Proceedings of the IFAC Workshop on Aerospace Guidance, Navigation and Flight Control Systems AGNFCS 09, Samara, Russia, 2009 (IFAC, 2009).

B. Andrievsky, N. Kuznetsov, G. Leonov, and A. Pogromsky, “Convergence based anti-windup design method and its application to flight control,” in Proceedings of the 4th International Congress on Ultra Modern Telecommunications and Control Systems ICUMT’2012, St. Petersburg, Russia, 2012 (IEEE, 2012), pp. 219–225.

A. Pavlov, A. Pogromsky, N. van de Wouw, and H. Nijmeijer, “Convergent dynamics, a tribute to Boris Pavlovich Demidovich,” Syst. Control Lett. 52, 257–261 (2004).

B. Andrievsky, N. Kuznetsov, and G. Leonov, “Convergence-based analysis of robustness to delay in antiwindup loop of aircraft autopilot,” in Proceedings of the IFAC Workshop on Advanced Control and Navigation for Autonomous Aeroespace Vehicles ACNAAV 2015, Seville, Spain, 2015, IFAC Proc. (IFAC-PapersOnline), Vol. 48, No. 9, 144–149 (2015).