Robust L ₁ filtering with pole constraint in a disk via parameter-dependent Lyapunov functions

The problem of robust L ₁ filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L ₁ performance constraint and pole constraint in a disk. The new robust L ₁ performance criteria and regional pole placement condition are obtained via parameter-dependent Lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L ₁ filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.