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Robust discrete variable structure control with finite-time approach to switching surface. (English) Zbl 0997.93017
A robust discrete variable structure control is developed for a class of linear discrete-time systems subject to input disturbance, measurement noise and uncertainty. First, a dead-beat to a switching surface for a nominal system is accomplished. Then the internal model principle is used for redesigning the equivalent control to deal with the input disturbance and measurement noise. Without the requirement of a matching condition, the uncertainty is also tackled by the equivalent control. Based on the concept of Lyapunov redesign, a switching control is proposed to improve the system performance. Some illustrative examples are also presented. The paper broadens the classical Lyapunov stability theory by studying the uniform asymptotic stability of invariant sets of time-varying non-differentiable systems. First, the notation used is introduced. Next, the relaxed smoothness properties of the systems are explained and various stability domains are defined. Two functional families $L(\cdot)$ and $E(\cdot)$ are used to separate the problem of existence of solutions of suitable differential equations from the stability problem. The main result is a new criteria for asymptotic stability domains of invariant sets. An analogous result for uniform asymptotic stability of invariant sets is also obtained.
##### MSC:
 93B12 Variable structure systems 93C55 Discrete-time control systems 93B51 Design techniques in systems theory 93D20 Asymptotic stability of control systems 34D35 Stability of manifolds of solutions of ODE
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##### References:
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