Robust sliding mode design for uncertain stochastic systems based on H_∞ control method

Abstract

SUMMARYIn this paper, the design of sliding mode control is addressed for uncertain stochastic systems modeled by Itô differential equations. There exist the parameter uncertainties in both the state and input matrices, and the unmatched external disturbance. The key feature of this work is the integration of sliding mode control method with H∞ technique such that the robustly stochastic stability with a prescribed disturbance attenuation level γ can be obtained. A sufficient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. Finally, a numerical simulation is presented to illustrate the proposed method.

Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

“…In , a kind of discretized Brownian motion was utilized to simulate the standard Brownian motion. In this paper, the system is simulated by using a similar approach.…”

Design of Robust Supertwisting Algorithm Based Second-Order Sliding Mode Controller for Nonlinear Systems with Both Matched and Unmatched Uncertainty

“…This strategy gives a major objective in control system design to attain stability in the presence of uncertainties [1][2][3][4][5]. The design of the SMC systems mainly consists of two steps: the choice of the sliding mode switching surface and the design of the sliding mode controller.…”

“…The design of the SMC systems mainly consists of two steps: the choice of the sliding mode switching surface and the design of the sliding mode controller. Moreover, SMC has believed significant amount of interest due to several advantages, such that fast convergence, high robustness, and invariance to certain internal system parameter variations and its implementation are easy [5][6][7][8][9]. On the other hand, the worst disadvantage of the SMC methodology is the chattering phenomenon.…”

Almost sure H ∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays

“…These systems include, but are not limited to, uncertain systems [25], [35], stochastic systems [15], [21], [24], nonlinear systems [3] and fuzzy systems [36]. For example, In [25], a special integral-type switching function is constructed to guarantee that the system dynamics lies on the specified sliding surface.…”

“…These systems include, but are not limited to, uncertain systems [25], [35], stochastic systems [15], [21], [24], nonlinear systems [3] and fuzzy systems [36]. For example, In [25], a special integral-type switching function is constructed to guarantee that the system dynamics lies on the specified sliding surface. Very recently, the SMC problem of Markovian jump systems (MJSs) has gained particular research interests because of their practical applications in a variety of areas [5], [6], [19], [20], [28], [33].…”