Filter design of discrete-time switched linear systems with time-varying parameters
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This paper addresses the filtering problem for a class of discrete-time switched linear parameter varying systems under average dwell time switching. The stability result for general discrete-time switched systems with average dwell time is first presented. A mode-dependent full-order parameterized filter is then designed and the corresponding existence conditions of such filters are derived via LMI formulation. The desired filter gains and the admissible switching signals are obtained for a given system decay degree such that the resulting filter error system is exponentially stable and has a guaranteed H ∞ performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.Keywords:
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This paper considers the finite-time stability and stabilization problem of discrete-time switched system with modedependent average dwell time. Firstly, a sufficient condition is proposed to guarantee the finite-time stability of discrete-time switched system. Secondly, a state feedback controller is designed to guarantee the finite-time stability of the corresponding closed-loop system based on LMIs toolbox of MATLAB. Finally, two examples are given to show the feasibility and effectiveness of results.
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Recently, a framework for controller design of sampleddata nonlinear systems via their approximate discrete-time models has been proposed in the literature. This framework naturally leads to investigation of families of parameterized discrete-time systems. In this paper we present a case-study in cascades-based control. That is, we show the utility of a theorem for stability of parameterized discrete-time cascades in the tracking control of the unicycle benchmark. This application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete-time parameterized systems and therefore motivates a formal study of parameterized discrete-time systems.
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Abstract This paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.
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A framework for controller design of sampled-data nonlinear systems via their approximate discrete time models has been established recently. Within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems. Further results that guarantee appropriate stability of the parameterized family of discrete-time systems that is used within this framework have been also established for systems with cascaded structure. A fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade. However, this is difficult to check in general. In this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check. These results further contribute to the toolbox for controller design of sampled-data nonlinear systems via their approximate discrete-time models.
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This paper addresses the exponential admissibility of a class of discrete-time switched singular systems with time-varying delay. By defining a properly constructed decay-rate-dependent Lyapunov function and using the average dwell time approach, a delay-dependent sufficient condition is derived for the system to be regular, causal and exponentially stable. The obtained results provide a solution to one of the basic problems in discrete-time switched singular time-delay systems, that is, to identify a switching signal for which the switched singular time-delay system is regular, causal and exponentially stable. Numerical example is given to demonstrate the effectiveness of the proposed results.
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Recently, a framework for controller design of sampleddata nonlinear systems via their approximate discretetime models has been proposed in the literature. This framework naturally leads to investigation of families of parameterized discrete-time systems. In this paper we present a case-study in cascades-based control. That is, we show the utility of a theorem for stability of parameterized discrete-time cascades in the tracking control of the unicycle benchmark. This application is fairly illustrative of the technical dierences and obstacles encountered in the analysis of discrete-time parameterized systems and therefore motivates a formal study of parameterized discrete-time systems.
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