Stability and L2 Gain Analysis of Discrete-Time Switched Systems

By Guisheng Zhai, Bo Hu, K. Yasuda, Anthony N. Michel. 2002

50 citations recorded by the source corpus.

In this paper, we investigate some qualitative properties for time-controlled switched systems consisting of several linear discrete-time subsystems. First, we study exponential stability of the switched system with commutation property, stable combination and average dwell time. When all subsystem matrices are commutative pairwise and there exists a stable combination of unstable subsystem matrices, we propose a class of stabilizing switching laws where Schur stable subsystems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. For more general switched system whose subsystem matrices are not commutative pairwise, we show that the switched system is exponentially stable if the average dwell time is chosen sufficiently large and the total activation time ratio between Schur stable and unstable subsystems is not smaller than a specified constant. Secondly, we use an average dwell time approach incorporated with a piecewise Lyapunov function to study the L2 gain of the switched system. We show that when all subsystems are Schur stable and achieve an L2 gain smaller than a positive scalar γ0, (1) if all subsystems have a common Lyapunov function in the sense of L2 gain, then the switched system achieves the same L2 gain γ0 under arbitrary switching; (2) if there does not exist a common Lyapunov function, then the switched system under an average dwell time scheme achieves a weighted γ0 gain 70, and the weighted L2 gain approaches normal L2 gain if the average dwell time is chosen sufficiently large.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0e74b0c02b03bfaf159cd3e956a5676d45277cbb

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In Control and Systems Engineering

Citations in the corpus

Analysis and design of switched normal systems (2006, background): “[4,24, 25,27] extended the consideration to stability analysis problems for switched systems composed of discrete-time subsystems.”
Quadratic stabilizability of switched linear systems with polytopic uncertainties (2003, background): “…depend on various environmental factors (Dayawansa and Martin 1999, Pettersson and Lennartson 2002), and that the methods of intelligent control design are based on the idea of switching between different controllers (Morse 1996, Liberzon and Morse 1999, Hu et al. 2000, 2002, Zhai et al. 2002 b).”
gain analysis for switched systems with continuous-time and discrete-time subsystems (2005, methodology): “In fact, it has been pointed out in Tan and Grigoriadis (2001a, b), Zhai et al. (2002a) that symmetric systems have good properties.”