A delay-kernel-dependent approach to saturated control of linear systems with mixed delays

Abstract

This article proposes a delay-kernel-dependent approach to deal with the saturated control problem of linear systems subject to mixed delays: discrete delay and distributed delay considering kernel. By combining the state vector and the distributed delay with kernel, a new polytopic representation strategy is used to cope with the nonlinear input saturation function. By choosing a Lyapunov–Krasovskii functional and applying an integral inequality both related to the distributed delay kernel, novel and less conservative results are provided to ensure the system stability. Finally, an example is simulated to display the advantages of the developed approach.