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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 $\dot x=f_i(x), \quad x_{k+1} =f_i (x_k)$ with $$i\in Q$$, $$Q$$ 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:
 93D30 Lyapunov and storage functions 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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