Stability For Discrete-time Stochastic Systems Research Articles

Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses

This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.

Finite-time Stochastic Stability and Stabilization for Uncertain Discrete-time Stochastic Systems with Time-varying Delay

This paper deals with the problems of finite-time stochastic stability and stabilization for discrete-time stochastic systems with parametric uncertainties and time-varying delay. Using the Lyapunov-Krasovskii functional method, some sufficient conditions of finite-time stochastic stability for a class of discrete-time stochastic uncertain systems are established in term of matrix inequalities. Then, a new criterion is proposed to ensure the closed-loop system is finite-time stochastically stable. The controller gain is designed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Receding Horizon Control-Based Stabilization of Discrete-Time Stochastic Systems With State Delay

The stabilization of receding horizon control (RHC) for a class of discrete-time stochastic systems with multiple state delay is concerned. Firstly, a cost function with the type of conditional expectation is designed. Secondly, the sufficient RHC stabilization condition has been obtained in terms of a linear matrix inequalities (LMI). And under some appropriate assumptions, it is shown that the stochastic system with state delay can be stabilized in the mean square sense if the terminal weighting matrices satisfy the given inequalities. Lastly, the explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Numerical examples show that the proposed RHC can effectively stabilize stochastic systems with state delay.

Almost sure stability and stabilization of discrete-time stochastic systems

As is well known, noise may play a stabilizing or destabilizing role in continuous-time systems. But, for analysis and design of discrete-time systems, noise is treated as disturbance in the literature. This paper studies almost sure stability of general n-dimensional nonlinear time-varying discrete-time stochastic systems and presents a criterion based on a numerical result derived from Higham (2001), which exploits the stabilizing role of noise in discrete-time systems. As an application of the established results, this paper proposes a novel controller design method for almost sure stabilization of linear discrete-time stochastic systems. The effectiveness of the proposed design method is verified with an example (an aircraft model subject to state-dependent noise), to which the existing results do not apply.

Hybrid Impulsive Control of Stochastic Systems with Multiplicative Noise Under Markovian Switching

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.

Critical stability and stabilization of discrete-time stochastic systems and its applications

In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-Belevitch-Hautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.

Stabilization of discrete-time stochastic systems via sliding mode technique

This paper considers the problem of sliding mode control for discrete-time stochastic systems with parameter uncertainties and state-dependent noise perturbation. An integral-like sliding surface is chosen and a discrete-time sliding mode controller is designed. The key feature in this work is that both the reachability of the quasi-sliding mode and the stability of system states are simultaneously analyzed, due to the existence of state-dependent noise perturbation. By utilizing an Lyapunov function involving system states and sliding mode variables, the sufficient condition for reachability is obtained. Finally, numerical simulation results are provided.