Nonlinear Stochastic Impulsive Systems Research Articles

Robust fuzzy control for nonlinear impulsive stochastic systems with Markov jumps and delay

This paper deals with the robust fuzzy control for a class of nonlinear impulsive stochastic delay systems with Markov jumps. The nonlinear systems under consideration are represented by the Takagi–Sugeno (T–S) fuzzy model because of the difficulty of solving that. Firstly, the criterion of mean square exponential stability is established. Secondly, based on the idea of parallel distributed compensation (PDC), the exponentially stabilized state-feedback fuzzy controllers are designed via solving a set of matrix inequalities. Finally, a numerical example is given to show the correctness and effectiveness of the theoretical results.

Stability of nonlinear impulsive stochastic systems with Markovian switching under generalized average dwell time condition

This paper examines the $p$-th moment globally asymptotic stability in probability and $p$-th moment stochastic input-to-state stability for a type of impulsive stochastic system with Markovian switching. By applying the generalized average dwell time approach, some novel sufficient conditions are obtained to ensure these stability properties. Furthermore, the coefficient of the Lyapunov function is allowed to be time-varying, which generalizes and improves the existing results. As corollaries, nonlinear restrictions on the drift and diffusion coefficients are used as substitutes for some previous conditions. Two examples are provided to illustrate the effectiveness of the theoretical results.

Stability properties of nonlinear stochastic impulsive systems with time delay

This article establishes mean square stability and stabilization for stochastic delay systems with impulses. Using Razumikhin methodology, two approaches, classical Lyapunov-based method and comparison principle, are proposed to develop sufficient conditions that guarantee the stability and stabilization properties. It is shown that if the continuous system is stable and the impulses are destabilizing, the impulses should not be applied frequently. On the other hand, if the continuous system is unstable, but the impulses are stabilizing, the impulses should occur frequently to compensate the continuous state growth. Numerical examples are also presented to clarify the proposed theoretical results.

State Estimation of Stochastic Impulsive System Via Stochastic Adaptive Impulsive Observer

AbstractThis paper develops stochastic adaptive impulsive observer (SAIO) for state estimation of stochastic impulsive systems. Proposed observer is applicable to linear and a class of nonlinear stochastic impulsive systems. In addition to stochastic noises, the observer considers effect of parametric uncertainty and estimates unknown parameters by suitable adaptation laws. Interestingly, for certain impulsive systems, SAIO gives continuous state estimations from a discrete sequence of system output measurements. New theorems related to stochastic impulsive systems' boundedness are also developed and utilized to prove the boundedness of SAIO state estimation errors. Presented simulation results illustrate the effectiveness of the observer.

Controllability of Nonlinear Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion

We consider the infinite-dimensional dynamical control systems described by nonlinear impulsive stochastic evolution differential equations. Sufficient conditions for the complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the reasonable assumption that the corresponding linear system is completely controllable.

Approximate controllability of nonlinear stochastic impulsive systems with control acting on the nonlinear terms

This paper is concerned with the approximate controllability of the stochastic impulsive system with control acting on the nonlinear terms. In the case that the nonlinear terms are dependent on the control, the control cannot be expressed explicitly and analysed. In this situation, we generate the control sequence by the approximate equations and give the properties of the control sequence and the driven solution sets. Some discussions on the assumptions are given to impose on the system. The Hausdorff measure is adopted to relax the requirement of the compactness condition. It is also shown that under some sufficient conditions the stochastic impulsive system is approximately controllable without the requirement of the controllability of the associated linear system. The results of this paper can be degraded into special cases and coincide with some existing ones.

Dissipativity Analysis and Synthesis for a Class of Nonlinear Stochastic Impulsive Systems

The dissipativity analysis and control problems for a class of nonlinear stochastic impulsive systems (NSISs) are studied. The systems are subject to the nonlinear disturbance, stochastic disturbance, and impulsive effects, which often exist in a wide variety of industrial processes and the sources of instability. Our aim is to analyse the dissipativity and to design the state-feedback controller and impulsive controller based on the dissipativity such that the nonlinear stochastic impulsive systems are stochastic stable and strictly(Q,S,R)-dissipative. The sufficient conditions are obtained in terms of linear matrix inequality (LMI), and a numerical example with simulation is given to show the correctness of the derived results and the effectiveness of the proposed method.

Constrained controllability of nonlinear stochastic impulsive systems

Constrained controllability of nonlinear stochastic impulsive systemsThis paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

Controllability of nonlinear impulsive Ito type stochastic systems

Controllability of nonlinear impulsive Ito type stochastic systemsIn this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

Controllability of non-linear impulsive stochastic systems

In this article, we consider the finite-dimensional dynamical control systems described by non-linear impulsive stochastic differential equations. Sufficient conditions for the complete and approximate controllability of non-linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable.

Controllability of nonlinear stochastic neutral impulsive systems

The impulsive differential equations provide a natural description of observed evolutionary processes, which are subject to short term perturbations acting instantaneously in the form of impulses. Uncertainty can be incorporated either as an expression of our lack of precise knowledge or as a true driving force. In the latter case it is useful to model the system by a stochastic or noise driven model which leads to the study of stochastic impulsive differential systems. In this paper, the notion of complete controllability for nonlinear stochastic neutral impulsive systems in finite dimensional spaces is introduced. Sufficient conditions ensuring the complete controllability of the nonlinear stochastic impulsive system are established. The results are obtained by using the Banach fixed point theorem. Several forms of integrodifferential impulsive systems are indicated. Two examples are discussed to illustrate the efficiency of the obtained results.