Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay

Hai Zhang,Wei Jiang,Jinde Cao

doi:10.1155/2013/567089

Abstract

This paper is concerned with the reachability and controllability of fractional singular dynamical systems with control delay. The factors of such systems including the Caputo’s fractional derivative, control delay, and singular coefficient matrix are taken into account synchronously. The state structure of fractional singular dynamical systems with control delay is characterized by analysing the state response and reachable set. A set of sufficient and necessary conditions of controllability for such systems are established based on the algebraic approach. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed criteria.

Highlights

Singular systems play important roles in mathematical modeling of real-life problems arising in a wide range of applications
In this paper, we investigate the reachability and controllability of fractional singular dynamical systems with control delay
The state structure of fractional singular dynamical systems with control delay has been characterized by analysing the state response and reachable set

Summary

Introduction

Singular systems play important roles in mathematical modeling of real-life problems arising in a wide range of applications. It should be emphasized that the control theory of fractional singular systems is not yet sufficiently elaborated, compared to that of fractional normal systems In this regard, it is necessary and important to study the controllability problems for fractional singular dynamical systems. To the best of our knowledge, there are no relevant reports on reachability and controllability of fractional singular dynamical systems as treated in the current literature. We consider the reachability and controllability of the following fractional singular dynamical systems with control delay: EcDαx (t) = Ax (t) + Bu (t) + Cu (t − τ) , t ≥ 0, u (t) = ψ (t) , −τ ≤ t ≤ 0,.

Preliminaries

State Response and State Reachability

Controllability Criteria

An Illustrative Example

Conclusions