A novel ℋ∞ filter design condition for discrete-time linear parameter-varying systems

This paper presents a novel condition for designing full-order parameter-dependent filters for discrete-time linear parameter-varying (LPV) systems. It is assumed that time-varying parameters are measured and can be used online. However, in scenarios where such parameters are unavailable, a robust filter can be designed. Notably, the filtering matrices are derived independently from the Lyapunov function, allowing for the use of parameter-dependent Lyapunov functions even in robust filter designs. The Lyapunov theory to design parameter-dependent filters with a guaranteed ℋ ∞ performance is employed, and the proposed conditions are formulated in the form of linear matrix inequalities. A feature of the proposed method is that filtering matrices are directly recovered from synthesis conditions, eliminating the need for variable changes. Numerical experiments demonstrate the efficacy of our proposed approach.