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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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