Dissipativity and stabilization for uncertain switched nonlinear systems with mixed delays

This paper is concerned with the dissipativity and exponential stabilization of uncertain switched nonlinear systems with mixed time-varying delays. It is assumed that the uncertainties investigated are norm-bounded. Furthermore, a novel multi-Lyapunov-Krasovskii functional is constructed and plays an important role in the study of stability and dissipativity. By utilizing Jensen’s inequality and average dwell time scheme, the solvable conditions of exponential stabilization and dissipativity with respect to quadratic supply rates are presented and formulated in terms of a set of linear matrix inequalities. Then, based on special operations of matrices, the state feedback controllers of uncertain switched nonlinear systems with mixed delays are designed to guarantee the stability of the switched systems. Finally, one numerical example is used to show the validity and potential of the proposed method.