Branicky, Michael S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. (English) Zbl 0904.93036 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) Cited in 605 Documents 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 PDF BibTeX XML Cite \textit{M. S. Branicky}, IEEE Trans. Autom. Control 43, No. 4, 475--482 (1998; Zbl 0904.93036) Full Text: DOI