General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach

Yiheng Wei,Qing Gao,Hamid Reza Karimi,Shu Liang,Yong Wang

doi:10.1155/2014/737495

Abstract

This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI) systems with the fractional commensurate order0<α<2. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI) are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with0<α<1. Furthermore, the results are extended to stabilize the FO-LTI systems with1≤α<2. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

Highlights

In recent years, fractional order systems (FOSs) have attracted considerable attention from control community, since many engineering plants and processes cannot be described concisely and precisely without the introduction of fractional order calculus [1,2,3,4,5,6]
This paper aims at finding the proper condition so that the resulting closed-loop system is asymptotically stable with the three types of output feedback controller (OFC)
Based on the equivalence transformation, the related results are generalized to the systems with 1 ≤ α < 2

Summary

Introduction

Fractional order systems (FOSs) have attracted considerable attention from control community, since many engineering plants and processes cannot be described concisely and precisely without the introduction of fractional order calculus [1,2,3,4,5,6]. Linear matrix inequality (LMI) is one of the most effective and efficient tools in controller design and a great deal of LMI-based methods of OFC design have been proposed over the last decade. These methods can be broadly classified into three categories: iterative algorithm [19, 20], singular value decomposition (SVD) method [21,22,23,24], and slack variable method [25, 26].

Objectives

Results

Conclusion