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Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. (English) Zbl 0904.93036

Hybrid systems are systems of the form

x ˙=f i (x),x k+1 =f i (x k )

with iQ, Q being a finite set of indices. Even if each system defined by f i (x) has the equilibrium at the origin stable, the switching might be such that for the “polysystem” the origin would not be stable. The stability is studied by using a set of switched Lyapunov functions (called multiple Lyapunov functions). Other properties such as the existence of a limit cycle and Bendixson-type theorems are discussed.

MSC:
93D30Scalar and vector Lyapunov functions
93C30Control systems governed by other functional relations