Abstract
The problem of robustl2-l∞filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on thel2-l∞performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficientl2-l∞performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robustl2-l∞filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.
Highlights
The uncertainty is unavoidable in practical engineering due to the parameter drafting, modeling error, and component aging
The robust l2-l∞ filtering has been studied for uncertain discrete-time systems with time-varying delay in this paper
The desired filter has been designed for the filtering error system with time-varying delay
Summary
The uncertainty is unavoidable in practical engineering due to the parameter drafting, modeling error, and component aging. The controllers or filtering obtained based on nominal systems cannot be employed to get the desired performance. Time-delay often exists in the practical engineering systems and is the main reason of the instability and poor performance of the systems. Time-delay systems have been widely studied during the past two decades [5,6,7]. In order to get less conservative results, more and more approaches have been proposed to develop delay-dependent conditions for discrete-time system with time-varying delay. Jensen’s inequality is proposed in [8]; delaypartitioning method is utilized in [9]; improved results are obtained by using convex combination approach in [10]
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