Robust L₂-L_x filtering with pole constraint in a disk via parameter-dependent Lyapunov functions

Addresses the design problems of robust L₂-L_∞ filters with pole constraint in a disk for uncertain continuous-time linear systems. The uncertain parameters are assumed to belong to convex bounded domains. The aim is to determine a stable linear filter such that the filtering error system possesses a prescribed L₂-L_∞ noise attenuation level and expected poles location. The filtering strategies are based on parameter-dependent Lyapunov stability results to derive new robust L₂ -L_∞ performance criteria and the regional pole placement conditions. From the proposed multi-objective performance criteria, we derive sufficient conditions for the existence of robust L₂ - L_∞ filters with pole constraint in a disk, and cast the filter design into a convex optimization problem subject to a set of linear matrix inequality constraints. This filtering method exhibits less conservativeness than previous results in the quadratic framework. The advantages of the filter design procedures are demonstrated by means of numerical examples.