Shorten, Robert; Ó Cairbre, Fiacre A proof of global attractivity for a class of switching systems using a non-quadratic Lyapunov approach. (English) Zbl 0992.93084 IMA J. Math. Control Inf. 18, No. 3, 341-353 (2001). The authors consider the switched system \[ \dot x+A(t)x \] where \(A(t)\) is piecewise constant and takes a finite number of values \(A_i\), \(i=1,\dots,m\). The exponential stability of this system is ensured by the existence of a common quadratic Lyapunov function \(x^TPx\) for all constituent system \[ \dot x=A_ix,\;i=i,\dots,m. \] Some new conditions for the existence of such a function are considered; the known conditions are weakened in the sense that upper triangularization of the \(A_i\) no longer needs to be performed via a common similarity transformation. Reviewer: Vladimir Răsvan (Craiova) Cited in 7 Documents MSC: 93D30 Lyapunov and storage functions 93B12 Variable structure systems 93D20 Asymptotic stability in control theory Keywords:asymptotic stability; switched system; exponential stability; common quadratic Lyapunov function Software:LMI toolbox PDFBibTeX XMLCite \textit{R. Shorten} and \textit{F. Ó Cairbre}, IMA J. Math. Control Inf. 18, No. 3, 341--353 (2001; Zbl 0992.93084) Full Text: DOI