Lyapunov Characterization for the Stability of Stochastic Control Systems

Abstract

Lyapunov-like characterization for the problem of input-to-state stability in the probability of nonautonomous stochastic control systems is established. We extend the well-known Artstein-Sontag theorem to derive the necessary and sufficient conditions for the input-to-state stabilization of stochastic control systems. Illustrating example is provided.

Path-Following Control Method for Surface Ships Based on a New Guidance Algorithm

“…A new hyperbolic guidance method for straight-line path-following control is presented in this paper. A Lyapunov function analysis [38] is used to prove the stability of this method. For curve guidance, based on the Lyapunov stability function, this paper presents a reverse stepping method to calculate heading rate command and make the system globally asymptotically stable, with a correction formula for current interference.…”

Stabilization of nonlinear stochastic systems without unforced dynamics via time--varying feedback

“…The main tools used in this paper are the stochastic Lyapunov stability theory introduced by Khasminskii in [13] combined with the stochastic La Salle invariance principle proved by Kushner [14] and the bounded feedback design technique for passive stochastic differential systems developed in [10]. The class of systems considered in this paper cannot be incorporated in the framework handled by the works exposed in [1]- [3] on the stabilization of time-varying stochastic systems developed in the past years. This paper is divided into four sections and is organized as follows.…”

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