Non-fragile Guaranteed Research Articles

Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems

Abstract This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Comments on ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’

This paper points out some technical errors in a recent paper that appeared in Transactions of the Institute of Measurement and Control entitled ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’ by Akshata Tandon and Amit Dhawan ( http://dx.doi.org/10.1177/0142331216667476 ). We reveal that the upper bound of the closed-loop cost function provided by their Lemma 4 is erroneous. Some critical issues associated with the system initial conditions assumed in their paper are highlighted. The closed-loop cost bound claimed by their Theorem 1 is found to be incorrect. The optimization problem formulated in their Theorem 2 for the selection of an optimal guaranteed cost controller is erroneous. Finally, the corrections over their results are made available.

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

ABSTRACTThis paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.

An LMI approach to non-fragile robust optimal guaranteed cost control of 2D discrete uncertain systems

This paper addresses the problem of non-fragile robust optimal guaranteed cost control for a class of two-dimensional discrete systems described by the general model with norm-bounded uncertainties. Based on Lyapunov method, a new linear matrix inequality (LMI)-based criterion for the existence of non-fragile state feedback controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select a non-fragile robust optimal guaranteed cost controller, which minimizes the upper bound of the closed-loop cost function. The merit of the proposed criterion in aspect of conservativeness over a recently reported criterion is demonstrated with the help of illustrative examples.

Non-fragile Robust Control for Singular Systems with Nonlinear Perturbation

This note discusses the problem of non-fragile robust control for singular systems with nonlinear structured perturbations. These perturbations are functions of time that occur in the system states and satisfy Lipschitz constraint. By means of the Linear Matrix Inequality (LMI) approach, the sufficient conditions of existence and design approaches are presented for the corresponding non-fragile robust controllers, as well as the non-fragile robust guaranteed cost controllers, respectively. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed approach.

Non-Fragile Robust Guaranteed Cost Control of 2-D Discrete Uncertain Systems Described by the General Models

The problem of non-fragile robust guaranteed cost control for a class of two-dimensional (2-D) discrete systems in the general model (GM) with norm-bound uncertainties is investigated. The purpose is to design a non-fragile state feedback controller such that the closed-loop system is asymptotically stable and the cost function value is not more than an upper bound for all admissible uncertainties. The cost function is proposed and an upper bound of the cost function is given. By using a linear matrix inequalities (LMIs) approach, a sufficient condition for the solvability of the problem is obtained. A desired non-fragile state feedback controller can be constructed by solving a set of LMIs. An example is provided to demonstrate the application of the proposed design method.