Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α

Yuanhua Li,Heng Liu,Hongxing Wang

doi:10.1155/2015/606048

Yuanhua Li, Heng Liu + Show 1 more

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https://doi.org/10.1155/2015/606048

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Abstract

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

Highlights

During the last two decades, the study of fractional-order control systems has received more and more attention
In [12], a new and effectively robust stability checking method was first proposed for fractional-order linear timeinvariant (FO-LTI) interval uncertain systems in terms of LMIs, and an analytical design of the stabilizing controllers for fractional-order dynamic interval systems was given
With the above motivation, based on the results of [12], the robust stability and stabilization problems of uncertain FO-LTI interval systems with the fractional-order α belonging to 1 ≤ α < 2 are further investigated in this paper

Summary

Introduction

During the last two decades, the study of fractional-order control systems has received more and more attention. In [12], a new and effectively robust stability checking method was first proposed for FO-LTI interval uncertain systems in terms of LMIs, and an analytical design of the stabilizing controllers for fractional-order dynamic interval systems was given. With the above motivation, based on the results of [12], the robust stability and stabilization problems of uncertain FO-LTI interval systems with the fractional-order α belonging to 1 ≤ α < 2 are further investigated in this paper. This paper is organized as follows: in Section 2, we present some preliminaries results on the fractional derivative, the linear algebra and the matrix theory.

Preliminaries

Main Results

Numerical Examples

Conclusion