Stabilizing Supervisory Control of Hybrid Systems Based on Piecewise Linear Lyapunov Functions 1 (original) (raw)
2000
In this paper, the stability of discrete-time piecewise linear hybrid systems is in- vestigated using piecewise linear Lyapunov functions. In particular, we consider switched discrete-time linear systems and we identify classes of switching sequences that result in stable trajectories. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. In the proposed approach, we assume that each individual subsystem is stable and admits a piece- wise linear Lyapunov function. Based on these Lyapunov functions, we compose "global" Lyapunov functions that guarantee stability of the switched linear system. A large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space.
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