Robust ℋ∞ memory filters for uncertain discrete-time linear systems

This paper is concerned with the problem of robust full-order ℋ_∞ filter design for uncertain discrete-time linear systems. The uncertainties 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 system output measures, 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_∞ filter design. Due to the extra dynamics, the robust memory filter is able to provide less conservative results in terms of the ℋ_∞ performance when compared to the memoryless case. Numerical examples are given to demonstrate the improvements of the proposed method.