Robust Nonfragile Controllers Design for Fractional Order Large-Scale Uncertain Systems with a Commensurate Order1&lt;α&lt;2

Jianyu Lin

doi:10.1155/2015/206908

Abstract

The paper concerns the problem of stabilization of large-scale fractional order uncertain systems with a commensurate order1<α<2under controller gain uncertainties. The uncertainties are of norm-bounded type. Based on the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale uncertain systems in both cases of additive and multiplicative gain perturbations are established by using the complex Lyapunov inequality. Moreover, the decentralized nonfragile controllers are designed. Finally, some numerical examples are given to validate the proposed method.

Highlights

In the past decades, a great deal of attention has been paid to the stability and stabilization of large-scale systems [1,2,3,4,5,6,7]
The nonfragile control problem has been an attractive topic in theory analysis and practical implement, because of perturbations often appearing in the controller gain, which may result in either the actuator degradations or the requirements for readjustment of controller gains
By solving the Linear Matrix Inequalities (LMI) (27), we derive the sufficient conditions on stabilizability via decentralized state feedback of the uncertain fractional order system under multiplicative gain perturbations

Summary

Introduction

A great deal of attention has been paid to the stability and stabilization of large-scale systems [1,2,3,4,5,6,7]. The robust resilient stabilization problem is to design a nonfragile state feedback controller such that the uncertain fractional order large-scale interconnected closedloop system with a commensurate order 1 < α < 2 is robustly stable for all admissible parameter uncertainties. Very few studies provide LMI conditions for the stability analysis of the fractional order large-scale interconnected system in the literature. The objective of the paper is to design a nonfragile controller which is robust to system uncertainties and resilient to controller gain variations for the fractional order large-scale interconnected systems with a commensurate order 1 < α < 2. Re() and Im() are corresponding to the real and imaginary parts of the matrix, respectively

Preliminaries and Problem Formulation

Numerical Examples

Conclusions