Kybernetika 61 no. 6, 752-761, 2025

A stochastic version of Vidyasagar theorem on the stabilization of interconnected systems

Patrick FlorchingerDOI: 10.14736/kyb-2025-6-0752

Abstract:

The purpose of this paper is to provide sufficient conditions for the feedback asymptotic stabilization in probability for a class of affine in the control nonlinear stochastic differential systems. In fact, under the assumptions stated in this paper we prove the existence of a control Lyapunov function that according to the stochastic version of Artstein's theorem guarantees the asymptotic stability in probability by means of a state feedback law that is smooth except eventually at the equilibrium. This result generalizes the well-known theorem of Vidyasagar concerning the feedback stabilization problem for interconnected control systems.

Keywords:

control Lyapunov function, asymptotic stability in probability, smooth state feedback law

Classification:

60H10, 93C10, 93D05, 93D15, 93E15

paper.pdf

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