Abstract
This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.
Highlights
Consider a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients described by dx1 = (d1 (t) x2 + f1 (x3)) dt + g1T (x3) dω, dx2 = (d2 (t) x3 + f2 (x4)) dt + g2T (x4) dω, (1)dxn−2 = (dn−2 (t) xn−1 + fn−2) dt + gnT−2 dω, dxn−1 = dn−1 (t) xndt, dxn = dn (t) udt, where x = (x1, . . . , xn)T ∈ Rn, u ∈ R are the measurable state and the input of system, respectively. xi = (xi, . . . , xn)T. ω is an r-dimensional standard Wiener process defined on a probability space (Ω, F, P), with Ω being a sample space,F being a filtration, and P being a probability measure
Note that the listed results above do not consider the stochastic noise. From both practical and theoretical points of view, it is more important to study the control of uppertriangular stochastic nonlinear systems with time-varying control coefficients
(i) This paper is the first result about state-feedback stabilization of upper-triangular stochastic nonlinear systems with time-varying control coefficients
Summary
Consider a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients described by dx1 = (d1 (t) x2 + f1 (x3)) dt + g1T (x3) dω, dx2 = (d2 (t) x3 + f2 (x4)) dt + g2T (x4) dω,. Note that the listed results above do not consider the stochastic noise From both practical and theoretical points of view, it is more important to study the control of uppertriangular stochastic nonlinear systems with time-varying control coefficients. In this paper, based on the low gain homogeneous domination technique, for system (1), we design a stabilization state-feedback controller, under which the closed-loop systems can be proved to be globally asymptotically stable in probability. (i) This paper is the first result about state-feedback stabilization of upper-triangular stochastic nonlinear systems with time-varying control coefficients.
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