Stochastic Nonlinear Time-delay Systems Research Articles

Robust filtering with stochastic nonlinearities and multiple missing measurements

This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [ 0 1 ] . Such a probabilistic distribution could be any commonly used discrete distribution over the interval [ 0 1 ] . The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the linear matrix inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.

Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters

This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.

A NEW LMI CONDITION FOR DELAY-DEPENDENT ROBUST STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS

This paper studies robust stability for a class of uncertain nonlinear stochastic time-delay systems. In terms of a linear matrix inequality, an improved delay-dependent condition guaranteeing that a stochastic delay system will be exponentially stable in the mean square is proposed. This condition is less conservative than existing ones in the literature and is demonstrated by means of an example.

Robust Fuzzy Design for Nonlinear Uncertain Stochastic Systems via Sliding-Mode Control

This paper deals with the sliding-mode control (SMC) problem for nonlinear stochastic time-delay systems by means of fuzzy approach. The Takagi-Sugeno (T-S) fuzzy stochastic time-delay model with parametric uncertainties and unknown nonlinearities is presented. A sufficient condition for the exponential stability in mean square of the sliding motion is also derived. Moreover, it is shown that when the linear matrix inequalities (LMIs) with equality constraint are feasible, the designs of both sliding surface and sliding-mode controller can be easily obtained via convex optimization. A simulation example illustrating the proposed method is given.

On stabilization for a class of nonlinear stochastic time-delay systems: A matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

Output feedback stabilization for a class of stochastic time-delay nonlinear systems

This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization via output feedback can be solved by a Lyapunov-based recursive design method.

H∞ analysis of nonlinear stochastic time-delay systems

Abstract In this paper, the H ∞ analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H ∞ analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L 2 gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H ∞ performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.

CONTROLLER DESIGN FOR A CLASS OF NONLINEAR STOCHASTIC SYSTEMS WITH TIME-DELAYS

In this paper, the stabilization problem is considered for a class of nonlinear continuous stochastic systems with state delays. The purpose of this problem is to design a state feedback controller such that the closed-loop system is exponentially stable (or exponentially ultimately bounded) in the mean square, for all admissible nonlinearities and time-delays. We first investigate the sufficient conditions for the nonlinear stochastic time-delay systems to be stable, and then derive the explicit expression of the desired controller gains. A numerical simulation example is provided to show the usefulness of the proposed design method.

Comments on “State Feedback Stabilization for a Class of Stochastic Time-Delay Nonlinear Systems”

In this note, we point out an error in the above paper (Y. Fu et al., IEEE Trans. Automat. Contr., vol. 48, pp. 282-286, Feb. 2003) which shows that the main result of that paper cannot stand.

State feedback stabilization for a class of stochastic time-delay nonlinear systems

This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization via state feedback can be solved by a Lyapunov-based recursive design method.