Finite-time Stabilization Of Stochastic Systems Research Articles

Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

Finite-time stabilization of stochastic systems with varying parameters

&lt;abstract&gt;&lt;p&gt;This research deals with the stabilization of the stochastic nonlinear systems. In order to achieve the asymptotic stability in probability with respect to unknown bounded disturbances, a control Lyapunov function is applied to present a modified Sontag's homogeneous controller. The obtained results reveal that the presented control achieves the desirable robust asymptotic stability in probability. The finite-time stability in probability for stochastic nonlinear systems is also discussed in this manuscript. Simulation examples are provided to demonstrate the effectiveness of the controllers.&lt;/p&gt;&lt;/abstract&gt;

On Design of Homogeneous Feedback Controllers for Finite-Time Stabilization of Stochastic Systems

On Design of Homogeneous Feedback Controllers for Finite-Time Stabilization of Stochastic Systems

On Stochastic Finite-Time Stabilization with Continuous State-Feedback Controllers

This paper investigates finite-time stabilization of stochastic systems with homogeneous feedback controllers. In the finite-time stabilization problems, chattering-like behavior usually appears in the input signals due to stochastic noises when homogeneous feedback controllers are designed by backstepping-like methods. This study investigates the causes of the chattering-like behavior that appears in the homogeneous feedback controllers. Moreover, we present design approaches of controllers for the finite-time stabilization of stochastic systems based on homogeneity, with the objective of reducing the chattering-like behavior. Finally, the validity of the proposed controllers is investigated based on numerical experiments.

New Results on Finite-time Stabilization for Stochastic Systems with Time-varying Delay

The paper deals with the problem of finite-time stabilization for stochastic systems with time-varying delay by defining a new criterion for finite-time stability. Firstly, by use of more appropriate Lyapunov-Krasovskii functional (LKF), the difficulties of finite-time stability confronted in system analysis and synthesis can be overcome. Then, a state feedback controller is constructed to guarantee the closed-loop system finite-time stable. New conditions for finite-time stability analysis as well as controller synthesis are established in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the main results.

Strong Solutions of Stochastic Differential Equations in Finite-Time Stabilization

This paper discusses the finite-time stabilization of stochastic systems. Because the finite-time stabilization requires the non-Lipschitz continuity of closed-loop systems, it is difficult to guarantee the existence of strong solutions of stochastic differential equations. This paper considers finite-time stabilizing feedback controllers such that closed-loop systems possess strong solutions. We provide a condition of the existence of such feedback controllers. The condition is given in the framework of control Lyapunov functions. Also, we provide an example of the finite-time stabilization where the existence of a strong solution is guaranteed.

Finite-Time Stabilization of Stochastic Systems With Partially Known Transition Probabilities

In this paper, the problem of finite-time stabilization for a class of uncertain Markov jump systems with partially known transition probabilities is investigated. The main aim of this paper is to derive the finite-time stabilization criteria for the underlying systems when the transition probabilities are partially known and to design a state feedback stabilizing controller such that the trajectories of the system stay within a given bound in a fixed time interval. Sufficient conditions for the existence of the desired controller are established with the linear matrix inequalities framework. A numerical example is used to illustrate the effectiveness of the developed theoretic results.