H? Gain Scheduling for Discrete-Time Systems with Control Delays and Time-Varying Parameters: a BMI Approach

Authors

Chaouki T. Abdallah
Renato A. Borges
Ricardo C. Oliveira
Pedro L. Peres

Document Type

Article

Publication Date

6-11-2008

Abstract

In this paper, the problem of gain scheduling for time-varying systems with time delays is investigated. By using a memory at the feedback loop, a discrete gain scheduled controller which minimizes an upper bound to the ,Hscrinfin performance of the closed loop system is determined. The design conditions, expressed in terms of bilinear matrix inequalities, are obtained from the Finsler's Lemma combined with the Lyapunov theory. The extra variables introduced by the Finsler's Lemma represent an alternative way in the search of better system behavior. The time-varying uncertainties are modeled using polytopic domains. The controller is obtained by the solution of an optimization problem formulated only in terms of the vertices of the polytope. No grids in the parametric space are used. Numerical examples illustrate the efficiency of the proposed approach.

Publisher

IEEE

Publication Title

2008 American Control Conference

ISSN

978-1-4244-2078-0

First Page

3088

Last Page

3093

DOI

10.1109/ACC.2008.4586967

Language (ISO)

English

Keywords

Lyapunov matrix equations, discrete time systems, time-varying systems

Recommended Citation

Abdallah, Chaouki T.; Renato A. Borges; Ricardo C. Oliveira; and Pedro L. Peres. "H? Gain Scheduling for Discrete-Time Systems with Control Delays and Time-Varying Parameters: a BMI Approach." 2008 American Control Conference (2008): 3088-3093. doi:10.1109/ACC.2008.4586967.