Robust H2 and H∞ memory filter design for linear uncertain discrete-time delay systems

This paper is concerned with the problems of robust full-order H 2 and H ∞ filter design for linear uncertain discrete-time systems with multiple state delays. The uncertain parameters affecting the matrices of the system are supposed to be time-invariant and to belong to a polytopic domain. The main novelty is the fact that the filter contains an arbitrary number of past states and past output measures of the system, yielding a filtering system with memory. Linear matrix inequality relaxations based on polynomially parameter-dependent Lyapunov matrices and slack variables are proposed for the H 2 and H ∞ filter design. Due to the extra dynamics introduced through the delayed states, the robust memory filter is able to provide less conservative results in terms of the H ∞ and the H 2 performance when compared to the memoryless case. Throughout the paper, the multiple delays are considered to be fixed and time-invariant, but an extension of the conditions to cope with unknown delays belonging to a given interval is also presented for both time-varying and time-invariant delay cases. Numerical examples are given to demonstrate the improvements of the proposed approach with respect to other methods from the literature. HighlightsFilter with arbitrary number of past states and output measures of the system.LMI relaxations based on polynomially parameter-dependent variables for filter design.Unknown (possibly time-varying) delays in an interval can affect the uncertain system.

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