On stabilizability and exact observability of stochastic systems with their applications

Authors:
Weihai Zhang;Bor-Sen Chen
Affiliations:
Department of Computer Science and Technology, Shandong Institute of Light Industry, Jinan 250100, China;Department of Electrical Engineering, National Tsing-Hua University, Hsin Chu 30043, Taiwan
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

This paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications. With the aid of the operator spectrum, a necessary and sufficient condition is given for the stabilizability of stochastic systems. Some new concepts such as unremovable spectrum and strong solution are introduced. An unremovable spectral theorem and a stochastic Popov-Belevith-Hautus Criterion for exact observability are presented. As applications, a comparison theorem for stochastic algebraic Riccati equations and a result on Lyapunov-type equations are obtained.