ROBUST DESIGN AND ROBUST STABILITY ANALYSIS OF ACTIVE NOISE CONTROL SYSTEMS

Abstract

The problem of designing robust active control systems is addressed in this paper. A variety of active control design problems are formulated as semidefinite programming (SDP) problems. An SDP problem is a convex optimization problem, consisting of a linear objective function subject to linear matrix inequality (LMI) constraints. First, an SDP formulation is presented for the design of multichannel LMS algorithms with limited-capacity secondary sources. Simulations show that this SDP formulation is an order of magnitude more computationally efficient than the usual non-linear constrained optimization formulations. Secondly, the design of robust LMS algorithms is presented as an SDP problem. These algorithms minimize the worst-case control error in the presence of unknown but norm-bounded perturbations on the secondary path model and on the primary field. Both the unstructured and structured perturbations cases are considered. The resulting controllers are exact solutions to the robust control design problem, except in the most general case of structured perturbations when they only minimize an upper bound on the worst-case residual control error. Thirdly, SDP formulations are proposed to compute guaranteed stability limits for the adaptive multiple-channel leaky LMS algorithm in the presence of both unstructured and structured perturbations on the secondary path. Monte Carlo simulations show that the obtained stability limits are much more reliable than previously used limits, based, for example, on the Gershgorin circle theorem.