Structured stabilisation of superlinear delay systems by bounded discrete-time state feedback control

Abstract

Taking different system structures in different Markovian modes into consideration, this paper studies the structured stabilisation of a class of superlinear hybrid stochastic delay systems by feedback control based on discrete-time state observations. The controller is designed in a bounded state area, rather than every observable state, in order to reduce control cost. The time delay is more general in terms of the classical differentiability assumption being relaxed. Compared with the existing papers on discrete-state-feedback stabilisation problem, a new method to estimate the difference between current-time state and discrete-time state is presented, as a result of which the conditions imposed on the underlying system and the control function are less restrictive. Meanwhile, the Lyapunov functional used in this paper is modified to adapt to this change. Finally, an application to stochastic structured neural networks is given to demonstrate the practicability of the developed theory.