1. Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion
- Author
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Zhang, Weihai, Zhang, Huanshui, and Chen, Bor-Sen
- Subjects
Liapunov functions -- Evaluation ,Riccati equation -- Evaluation ,Stochastic analysis -- Methods - Abstract
In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and detectability, such as stochastic Popov--Belevitch--Hautus Criterion for exact detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic [H.sub.2]/[H.sub.[infinity]] control with state- and control-dependent noise is also investigated, which extends and improves the recently published results. Index Terms--Exact detectability, generalized algebraic Riccati equation (GARE), spectrum, stabilization, stochastic linear quadratic regulator, [H.sub.2]/[H.sub.[infinity]] control.
- Published
- 2008