Feedback stabilization of stochastic nonlinear composite systems
The goal of this paper is to extend the result of \textit{A. Saberi}, \textit{P. V. Kokotovic} and \textit{H. J. Sussmann} [SIAM J. Control and Optimization 28, 1491-1503 (1990; Zbl 0719.93071)] to the stochastic system of the form \[ dx_ t= f(x_ t, y_ t)dt+ g(x_ i, y_ t) dw_ t, \qquad dy_ t= (Ay_ t+ Bu)dt, \] where \(g(x,y)= g(x,0)+ H(x,y) Cy\), \(w_ t\) being a standard Wiener process. It is supposed that \(x_ t\equiv 0\) is globally asymptotically stable in probability (G.A.S.P.) for \[ dx_ t= f(x_ t, 0)dt+ g(x_ t, 0)dw_ t. \] With these conditions it is proved that there exists a control \(u\) such that the corresponding closed-loop system is G.A.S.P. too.
scientific article; zbMATH DE number 612158