Generalized Quadratic Stability for Perturbated Singular Systems

This paper considers the generalized quadratic stability problem for continuous-time singular systems with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular systems is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach is illustrated by a numerical example.