A partially delay-dependent and disordered controller design for discrete-time delayed systems

This paper considers the stabilization problem for a class of discrete-time delayed systems by exploiting a partially delay-dependent controller whose gains suffer a disordering phenomenon simultaneously. Two stochastic variables are used to describe the partially delay-dependent and disordering properties, which are not independent, and referred to the original operation modes here. By introducing an augmented Markov chain, the corresponding closed-loop system is transformed into a Markovian jump system with four new operation modes (NOMs). Based on the proposed model, a kind of controller depending on NOMs is firstly proposed with linear matrix inequalities forms. Moreover, without designing a controller containing NOMs directly, another kind of stabilizing controller referring to one depending on original operation modes is developed, which is composed of a series of NOM-dependent controllers and satisfies a minimum variance approximation. Finally, two numerical examples are used to demonstrate the utility and superiority of the proposed methods. Copyright (c) 2016 John Wiley & Sons, Ltd.