IQC based robust stability verification for a networked system with communication delays
Tóm tắt
In this paper, we consider robust stability analysis of a networked system with uncertain communication delays. Each of its subsystems can have different dynamics, and interconnections among its subsystems are arbitrary. It is assumed that there exists an uncertain but constant delay in each communication channel. Using the so called integral quadratic constraint (IQC) technique, a sufficient robust stability condition is derived utilizing a sparseness assumption of the interconnections, and a set of decoupled robustness conditions are further derived which depend only on parameters of each subsystem, the subsystem connection matrix (SCM) and the selected IQC multipliers. These characteristics result in an evident improvement of computational efficiency for robustness verification of the networked system with delay uncertainties, which is illustrated by some numerical results.
Tài liệu tham khảo
D’Andrea R, Dullerud G E. Distributed control design for spatially interconnected systems. IEEE Trans Automat Contr, 2003, 48: 1478–1495
Langbort C, Chandra R S, D’Andrea R. Distributed control design for systems interconnected over an arbitrary graph. IEEE Trans Automat Contr, 2004, 49: 1502–1519
Zhou T. On the stability of spatially distributed systems. IEEE Trans Automat Contr, 2008, 53: 2385–2391
Fang H, Antsaklis P J. Distributed control with integral quadratic constraints. In: Proceedings of the 17th IFAC World Congress, Seoul, 2008. 574–580
Andersen M S, Pakazad S K, Hansson A, et al. Robust stability analysis of sparsely interconnected uncertain systems. IEEE Trans Automat Contr, 2014, 59: 2151–2156
Zhou T, Zhang Y. On the stability and robust stability of networked dynamic systems. IEEE Trans Automat Contr, 2016, 61: 1595–1600
Megretski A, Treil S. Power distribution inequalities in optimization and robustness of uncertain systems. J Math Syst, 1993, 3: 301–319
Megretski A, Rantzer A. System analysis via integral quadratic constraints. IEEE Trans Automat Contr, 1997, 42: 819–830
Kao C Y, Rantzer A. Stability analysis of systems with uncertain time-varying delays. Automatica, 2007, 43: 959–970
Kao C Y. On stability of discrete-time LTI systems with varying time delays. IEEE Trans Automat Contr, 2012, 57: 1243–1248
Pfifer H, Seiler P. Integral quadratic constraints for delayed nonlinear and parameter-varying systems. Automatica, 2015, 56: 36–43
Seiler P. Stability analysis with dissipation inequalities and integral quadratic constraints. IEEE Trans Automat Contr, 2015, 60: 1704–1709
Fridman E, Shaked U. An improved stabilization method for linear time-delay systems. IEEE Trans Automat Contr, 2002, 47: 1931–1937
Kharitonov P L, Zhabko A P. Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 2003, 39: 15–20
Summers E, Arcak M, Packard A. Delay robustness of interconnected passive systems: an integral quadratic constraint approach. IEEE Trans Automat Contr, 2013, 58: 712–724
Massioni P, Verhaegen M. Distributed control for identical dynamically coupled systems: a decomposition approach. IEEE Trans Automat Contr, 2009, 54: 124–135
Eichler A, Hoffmann C,Werner H. Robust stability analysis of interconnected systems with uncertain time-varying time delays via IQCs. In: Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, 2013. 2799–2804
Eichler A, Werner H. Improved IQC description to analyze interconnected systems with time-varying time-delays. In: Proceedings of American Control Conference, Chicago, 2015. 5402–5407
Wang Z K, Zhou T. Robust stability analysis of networked dynamic systems with uncertain communication delays. In: Proceedings of the 36th Chinese Control Conference, Dalian, 2017. 7684–7689
Willems J. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans Automat Contr, 1971, 16: 621–634
Rantzer A. On the Kalman-Yakubovich-Popov lemma. Syst Control Lett, 1996, 28: 7–10
Zhou T. Coordinated one-step optimal distributed state prediction for a networked dynamical system. IEEE Trans Automat Contr, 2013, 58: 2756–2771
Zhou T. On the controllability and observability of networked dynamic systems. Automatica, 2015, 52: 63–75
Zhou K M, Doyle J C, Glover K. Robust and Optimal Control. Upper Saddle River: Prentice-Hall, 1996. 239–260
Andersen M S, Hansson A, Pakazad S K, et al. Distributed robust sability analysis of interconnected uncertain systems. In: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, 2012. 1548–1553
Benson S J, Ye Y. DSDP5 User Guide-Software for Semiderfinite Programming. Technical Report ANL/MCS-TM-277. 2005