Mixed L2-L∞/H∞ filtering for uncertain linear systems: An LMI approach

The problem of full-order mixed L₂-L∞/H∞ performance filtering design for uncertain linear systems is addressed in this paper. The uncertain parameters are assumed to belong to convex bounded domains (i.e., polytope type uncertainty). The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded, using a mixed L₂-L∞/H∞ performance index as criterion. In the mixed L₂-L∞/H∞ filtering design, an upper bound to the peak value of the filtering error over all the energy bounded noise signals is minimized while an H∞ constraint is assured. The conditions for the existence of such a robust filter are provided in terms of linear matrix inequalities-LMIs, allowing the use of standard convex optimization procedures to solve the problem. Both continuous- and discrete-time systems are considered. The formulation presented is illustrated by one example