A necessary and sufficient condition for ℋ- index of linear time-varying systems

Author

Li, Xiaobo ; Liu, Hugh H T

Author_Institution

Inst. for Aerosp. Studies, Univ. of Toronto, Toronto, ON, Canada

fYear

2010

fDate

15-17 Dec. 2010

Firstpage

4393

Lastpage

4398

Abstract

The increasing interests in H_- index leads to some recent development in time domain investigation. This paper presents a necessary and sufficient condition of H_- index in a finite time horizon for linear time-varying systems. It shows that the existence of a lower bound of H_- index is equivalent to the existence of a certain backward differential Riccati equation. When applied to a linear time-invariant system with infinite time horizon, the result leads to an identical one given in frequency domain study in terms of algebraic Riccati equation. Detailed discussions of the property and special cases are presented. Finally, an example is given to illustrate the main results.

Keywords

H^∞ control; Riccati equations; differential equations; linear systems; robust control; time-varying systems; H_- index; algebraic Riccati equation; backward differential Riccati equation; finite time horizon; infinite time horizon; linear time-varying systems; robust control; Fault detection; Frequency domain analysis; Indexes; Riccati equations; Sensitivity; Time domain analysis; Time varying systems; ℋ- index; Fault detection; differential Riccati equation; timevarying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2010 49th IEEE Conference on

Conference_Location

Atlanta, GA

ISSN

0743-1546

Print_ISBN

978-1-4244-7745-6

Type

conf

DOI

10.1109/CDC.2010.5718038

Filename

5718038