Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

Angeli, 2002, A Lyapunov approach to incremental stability properties, IEEE Transactions on Automatic Control, 47, 410, 10.1109/9.989067 Boyd, 1994, Linear matrix inequalities in system and control theory Chesi, 2010, LMI techniques for optimization over polynomials in control: a survey, IEEE Transactions on Automatic Control, 55, 2500, 10.1109/TAC.2010.2046926 Chesi, 2013, Sufficient and necessary LMI conditions for robust stability of rationally time-varying uncertain systems, IEEE Transactions on Automatic Control, 58, 1546, 10.1109/TAC.2012.2229840 Chesi, G., Garulli, A., Tesi, A., & Vicino, A. (2002). Homogeneous polynomial Lyapunov functions for robust stability analysis of LFR systems. Technical report, Universitá di Siena, Siena, Italy. Chesi, 2004, Robust analysis of LFR systems through homogeneous polynomial Lyapunov functions, IEEE Transactions on Automatic Control, 49, 1211, 10.1109/TAC.2004.831152 2000, Advances in Linear Matrix Inequality Methods in Control Fromion, 1997, Some results on the behavior of Lipschitz continuous systems, 2011 Fromion, 2001, The weighted incremental norm approach: from linear to nonlinear H∞ control, Automatica, 37, 1585, 10.1016/S0005-1098(01)00106-6 Fromion, 1999, Nonlinear performance of a PI controlled missile: an explanation, International Journal of Robust and Nonlinear Control, 9, 485, 10.1002/(SICI)1099-1239(19990715)9:8<485::AID-RNC417>3.0.CO;2-4 Garulli, 2013, Global stability and finite L2m-gain of saturated uncertain systems via piecewise polynomial Lyapunov functions, IEEE Transactions on Automatic Control, 58, 242, 10.1109/TAC.2012.2205449 Hassibi, 1998, Quadratic stabilization and control of piecewise-linear systems, 3659 2005, vol. 312 Hovd, 2013, Relaxing PWQ Lyapunov stability criteria for PWA systems, Automatica, 49, 667, 10.1016/j.automatica.2012.10.013 James, 1993, A partial differential inequality for dissipative nonlinear systems, Systems & Control Letters, 21, 315, 10.1016/0167-6911(93)90074-G James, 1995, Numerical approximation of the H∞ norm for nonlinear systems, Automatica, 31, 1075, 10.1016/0005-1098(94)00161-B Johansson, 2003, vol. 284 Johansson, 1998, Computation of piecewise quadratic Lyapunov functions for hybrid systems, IEEE Transactions on Automatic Control, 43, 555, 10.1109/9.664157 Löfberg, 2004, YALMIP : A toolbox for modeling and optimization in MATLAB Lohmiller, 1998, On contraction analysis for non-linear systems, Automatica, 34, 683, 10.1016/S0005-1098(98)00019-3 Morinaga, 2004, Performance analysis of control systems with input constraints via piecewise quadratic storage functions, Asian Journal of Control, 6, 34, 10.1111/j.1934-6093.2004.tb00182.x Papachristodoulou, 2005, A tutorial on sum of squares techniques for systems analysis, 2686 Parrilo, 2000 Parrilo, 2003, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, 96, 293, 10.1007/s10107-003-0387-5 Pavlov, 2007, On convergence properties of piecewise affine systems, International Journal of Control, 80, 1233, 10.1080/00207170701261978 Pavlov, 2006, Uniform output regulation of nonlinear systems - a convergent dynamics approach Prajna, 2003, Analysis of switched and hybrid systems - beyond piecewise quadratic methods, 2779 Rantzer, 2000, Piecewise linear quadratic optimal control, IEEE Transactions on Automatic Control, 45, 629, 10.1109/9.847100 Romanchuk, 1996, Characterization of the Lp incremental gain for nonlinear systems, 3270 Romanchuk, 1999, Incremental gain analysis of piecewise linear systems and application to the antiwindup problem, Automatica, 35, 1275, 10.1016/S0005-1098(99)00023-0 Waitman, 2018 Waitman, 2016, Incremental L2-gain analysis of piecewise-affine systems using piecewise quadratic storage functions, 1334 Willems, 1971, The analysis of feedback systems Willems, 1972, Dissipative dynamical systems — Part I: General theory, Archive for Rational Mechanics and Analysis, 45, 321, 10.1007/BF00276493 Zames, 1963, Functional analysis applied to nonlinear feedback systems, IEEE Transactions on Circuit Theory, 10, 392, 10.1109/TCT.1963.1082162 Zames, 1966, On the input-output stability of time-varying nonlinear feedback systems — Part I: Conditions derived using concepts of loop gain, conicity, and positivity, IEEE Transactions on Automatic Control, 11, 228, 10.1109/TAC.1966.1098316 Zames, 1966, On the input-output stability of time-varying nonlinear feedback systems — Part II: Conditions involving circles in the frequency plane and sector nonlinearities, IEEE Transactions on Automatic Control, 11, 465, 10.1109/TAC.1966.1098356