H∞ control for linear descriptor systems with non-differentiable delays in both state and observation

Abstract

© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. This paper deals with the problem of (Formula presented.) control for linear descriptor systems with time-variable delay. The delay function, which is non-differentiable, appears in both the state and observation. For stability, appropriate Lyapunov–Krasovskii functionals are constructed to eliminate the derivative calculating of the delay function and utilize smaller number of linear matrix inequality decision variables. The proposed functionals are employed to derive new delay-dependent sufficient conditions for admissibility of the unforced descriptor closed-loop system. For (Formula presented.) control, we design state feedback controllers which make the descriptor closed-loop system admissible with a maximum (Formula presented.) disturbance attenuation level. A numerical example with simulation is given to illustrate the effectiveness of the proposed method.