Stability analysis of singular systems
This paper aims to outline a general stability theory based on the Lyapunov direct method for singular systems of the form (*) \(P(t,x)\dot x=f(t,x)\), where \(x\in {\mathbb{R}}^ n\) and \(f\in {\mathbb{R}}^ k\). Thus, P is in general a rectangular matrix and, when \(k=n\), P is allowed to be singular. In particular, (*) cannot be reduced in general to an usual state-space model. System (*) is considered under assumptions which ensure existence of solutions, but uniqueness is not assumed. This and other features of (*), cause the necessity of redefining in an appropriate way the classical notions of stability and asymptotic stability. A construction of a Lyapunov function candidate is presented.
scientific article; zbMATH DE number 4128740
scientific article