PASSIVITY ANALYSIS AND PASSIFICATION FOR UNCERTAIN SIGNAL-PROCESSING SYSTEMS

The problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers, decision feedba ck equalizers, and digital and analog filters, Equally important is th e problem of passification, where a compensator needs to be designed f or a given system to become passive. This paper considers these two pr oblems for a large class of systems that involve uncertain parameters, time delays, quantization errors, and unmodeled high-order dynamics. By characterizing these and many other types of uncertainty using a ge neral tool called integral quadratic constraints (IQC's), we present s olutions to the problems of robust passivity analysis and robust passi fication, More specifically, for the analysis problem, we determine if a given uncertain system is passive for all admissible uncertainty sa tisfying the IQC's, Similarly, for the problem of robust passification , we are concerned with finding a loop transformation such that a part icular part of the uncertain signal processing system becomes passive for all admissible uncertainty. The solutions are given in terms of th e feasibility of one or more linear matrix inequalities (LMI's), which can be solved efficiently.