Robust Control of Discrete‐time Singular Systems via Integral Sliding Surface

Abstract

In this paper, the sliding mode control for a class of uncertain discrete-time singular system with H ∞ performance constraint is studied. By taking the singular matrix E into consideration, a new type of integral sliding mode surface is firstly introduced, based on which a sufficient condition is derived to guarantee the sliding mode dynamics admissible with a given -level disturbance attenuation of the unmatched disturbance. A controller law is also given to keep the system trajectory staying in a neighborhood of the ideal sliding surface. Finally, a numerical example is given to show the effectiveness of the proposed approach.

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

“…In this paper, ±30% unknown model uncertainties are considered. The unknown model uncertainties ΔA i and ΔB i are random matrixes and of the form [36,[59][60][61][62]:…”

Discrete‐time systems sliding mode switching hyperplane design: A survey

“…[22][23][24][25][26][27] Other proposed techniques include, for example, linear Lyapunov equation approach, 28 H ∞ robust scheme, 29 or output feedback min-max controllers methodologies. [30][31][32] Some developments deal with particular types of VSC such as integral VSC-SM 21,[33][34][35][36] and other approaches have proposed the design of nonlinear surfaces to improve transient performance of discrete-time uncertain systems 37 or to obtain high speed response in delayed discrete-time linear systems. 38 A recent work 39 introduces a generic and flexible design proposal applicable to discrete-time mulitvariable linear systems.…”

“…Thus, C parameters can be obtained estimating the feedback matrix of the reduced-order system presented in (36). For this example, the following function in MATLAB was used: ] .…”

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

“…Especially, for discrete-time T-S fuzzy systems, results devoted to SOF control can be found in [5,12,18,19,21,23,24]; and especially, in [4] and [12], where a fuzzy weighting-dependent Lyapunov function (FWDLF) has been used. At last, some performances are generally to be added, H ∞ attenuation being one of the most widely used for T-S systems [8,[10][11][12][13]17,19,20,22,[25][26][27][28][29][30]. For real-time control, another important issue is the physical limitations of the actuators, such as input bounds and/or rate saturation constraints.…”