Further results on stability and exact observability of linear stochastic systems

A new criterion is proposed for exact observability of linear stochastic systems. As applications of it, the effects of exact observability due to state/output feedback are investigated. In addition, under the conditions of stability and exact observability, we discuss the property of a set defined by the generalized Lyapunov equations. Finally, with the aid of spectrum technique, we introduce a new concept - essential instability, for which, a necessary condition is also established.

[1]  Bor-Sen Chen,et al.  Stochastic H2/H∞ control with state-dependent noise , 2004, IEEE Trans. Autom. Control..

[2]  D. Hinrichsen,et al.  Stochastic H∞ , 1998 .

[3]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[4]  D. Hinrichsen,et al.  Stochastic $H^\infty$ , 1998 .

[5]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[6]  V. Ugrinovskii.  Robust H∞ infinity control in the presence of stochastic uncertainty , 1998 .

[7]  I. Petersen,et al.  Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty , 1997 .

[8]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[9]  Weihai Zhang,et al.  Infinite horizon stochastic H2/Hºº control for discrete-time systems with state and disturbance dependent noise. , 2008 .

[10]  Vasile Dragan,et al.  Stochastic observability and applications , 2004, IMA J. Math. Control. Inf..

[11]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[12]  Toader Morozan,et al.  Stability and control for linear systems with jump Markov perturbations , 1995 .

[13]  Bor-Sen Chen,et al.  On stabilizability and exact observability of stochastic systems with their applications , 2023, Autom..

[14]  Bor-Sen Chen,et al.  Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion , 2008, IEEE Transactions on Automatic Control.

[15]  J. D. Val,et al.  On the observability and detectability of continuous-time Markov jump linear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Jan C. Willems,et al.  Feedback stabilizability for stochastic systems with state and control dependent noise , 1976, Autom..

[17]  Thomas Kailath,et al.  Linear Systems , 1980 .