Gain-scheduled filtering for linear parameter-varying systems using inexact scheduling parameters with bounded variation rates

This paper is concerned with the problem of full-order H₂ linear parameter-varying filter design for continuous-time systems with bounded rate of variations under the condition that the scheduling parameters do not exactly fit the real ones. The scheduling parameters and their derivatives are supposed to belong to polytopes with known vertices. The synthesis conditions are formulated in terms of parameter-dependent bilinear matrix inequalities by means of parameter-dependent Lyapunov function and introducing some extra variables for the filter design. An iterative procedure is presented to cast the bilinear matrix inequalities problem into a linear matrix inequality optimization problem. The design of robust filters for both time-varying and time-invariant systems can be viewed as particular cases of the proposed method. The merit of the method presented in this paper lies in two fields. The first pertains to dealing with the measurement uncertainty in a less conservative manner than available approaches in the gain-scheduled filtering problem. The second is to provide more efficient methods than the existing ones in the literature for the robust filter design.