A semistabilizability/semidetectability approach to semistable H2 and H∞ control problems

Author

Hui, Qing ; Liu, Zhenyi

Author_Institution

Dept. of Mech. Eng., Texas Tech Univ., Lubbock, TX, USA

fYear

2011

fDate

28-30 Sept. 2011

Firstpage

566

Lastpage

571

Abstract

A new semistable H₂ and H_∞ control framework is developed to address the robust optimal control issues of linear semistable control systems subject to white noise. To do this, a new notion of semistabilizability/semidetectability is proposed as a means to connecting semistability with the Lyapunov equation based technique. With this new notion, we develop a semistable H₂ and H_∞ control theory by exploiting the properties of semistability. Necessary and sufficient conditions for semistability of the closed-loop system have been derived in terms of the Lyapunov equation and semidetectability. Based on these results, we propose a convex optimization technique to solve the semistable H₂ and H_∞ control design.

Keywords

H^∞ control; H² control; Lyapunov matrix equations; closed loop systems; control system synthesis; convex programming; linear systems; multi-agent systems; multi-robot systems; robust control; white noise; H_∞ control problem design; H₂ control problem design; Lyapunov equation based technique; closed-loop system; convex optimization technique; linear semistable control systems; robust optimal control; semistabilizability-semidetectability approach; white noise; Control design; Convex functions; Eigenvalues and eigenfunctions; Equations; Optimal control; Protocols; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Conference_Location

Monticello, IL

Print_ISBN

978-1-4577-1817-5

Type

conf

DOI

10.1109/Allerton.2011.6120217

Filename

6120217