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

Branicky, Michael S.

IEEE Trans. Autom. Control 43, No. 4, 475-482 (1998).

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)

Keywords:

hybrid systems; switching; switched Lyapunov functions; limit cycle