##
**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.

Reviewer: V.Răsvan (Craiova)

### 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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\textit{M. S. Branicky}, IEEE Trans. Autom. Control 43, No. 4, 475--482 (1998; Zbl 0904.93036)

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