An LMI formulation for the estimation-based approach to the design of adaptive filters

We present a linear matrix inequalities (LMI) formulation for the estimation-based approach to the design of adaptive FIR and IIR filters. LMI provide a convenient framework for the synthesis of multiobjective (H_2/H∞) control problems. Therefore, the H∞ disturbance attenuation criterion in the estimation-based adaptive algorithm can be easily augmented with the appropriate H2 performance constraints. The question of internal stability of the overall system is also directly addressed as a by-product of the Lyapunov-based nature of the LMI formulation. We use an active noise cancellation scenario to study the main features of the proposed LMI solution.