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

Abstract

Summary 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 © 2016 John Wiley & Sons, Ltd.

Stabilization of Markovian Jump Systems Via a Partially Mode-Dependent Controller of Dwell Times

“…This completes the proof. Remark 2: Compare with the existing partially modedependent method [35], the dwell times are included and play important roles, which could lead to less conservative results. Moreover, it also contains mode-dependent and mode-independent cases special ones, which is analyzed by a mode-dependent Lyapunov function.…”

“…It was actually an absolute method. In order to bridge the above two methods, a kind of partially mode-dependent controller is proposed in [35]. However, it is said that the introduced Bernoulli variable was a traditional one, whose two states occur instantaneously.…”

“…In [28], mismatches between the modes of systems and the modes of controllers were described by using a hidden Markov model. Particularly, in [35], a kind of partially modedependent controller was designed by introducing Bernoulli variables. It was found that the mode-independent controller is instantaneous.…”

Restricted Stabilization of Markovian Jump Systems Based on a Period and Random Switching Controller

“…Moreover, more information about the correlation between modes r t andr t are further considered and will be less conservative than controller (4) referred in [30], [31]. Thirdly, but not the last, in contrast to controllers (3) and (5) having fast switchings even instantaneously in [32], [33], the switching of (6) is more slower though r t and α(t) are fast switchings. Such a slower switching will lead to less damage to equipment or system and have a wider application scope.…”

“…Because it ignored operation mode totally even it is available sometimes, it is said to be an absolute approach. Recently, a kind of partially mode-dependent method was presented in [32] and bridged the above two cases, where a Bernoulli variable was introduced. By applying the polytopic uncertainty method to a controller, the fault-tolerant control of MJSs was considered in [34].…”