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Zbl 0953.93073
Tsinias, J.
Stochastic input-to-state stability and applications to global feedback stabilization.
(English)
[J] Int. J. Control 71, No.5, 907-930 (1998). ISSN 0020-7179; ISSN 1366-5820/e

The author considers the stochastic composite system described by the following stochastic differential Ito equations $$\Sigma_1 :dx =f_1 (x,u)dt+ g_1(x,u) dw(t)$$ $$\Sigma_2: dy=f_2 (x,y,u)dt +g_2(x,y,u) dw(t)$$ where $(x,y) \in\bbfR^n \times\bbfR^k$ are the vectors of state, $u\in \bbfR^m$ is the control (input) vector, $f_i,g_i, i=1,2$ are nonlinear vector functions of appropriate dimensions and $w\in\bbfR$ is a standard Wiener process. \par The author introduces new definitions of stochastic $\gamma$-input to state stability and derives sufficient conditions for global stabilization in two cases, i.e., by means of output (linear and bounded) static feedback and by a dynamic feedback controller.
[L.Socha (Katowice)]
MSC 2000:
*93E15 Stochastic stability
93D15 Stabilization of systems by feedback
93D25 Input-output approaches to stability of control systems
93A15 Large scale systems

Keywords: stochastic stability; large scale systems; input to state stability; stochastic composite system; global stabilization; dynamic feedback

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