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Zbl 0904.93036
Branicky, Michael S.
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems.
(English)
[J] IEEE Trans. Autom. Control 43, No.4, 475-482 (1998). ISSN 0018-9286

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.
[V.Răsvan (Craiova)]
MSC 2000:
*93D30 Scalar and vector Lyapunov functions
93C30 Control systems governed by other functional relations

Keywords: hybrid systems; switching; switched Lyapunov functions; limit cycle

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