A convex characterization of parameter-dependent H/sub ∞/ controllers

Abstract

An important class of linear time-varying systems consists of plants where the state-space coefficients are fixed functions of certain time-varying physical parameters /spl theta/. Small gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often unduly conservative when the parameters /spl theta/ undergo large variations during system operation. In particular, higher performance can be achieved by control laws which incorporate available measurements of /spl theta/ and therefore adjust to the current plant dynamics. This paper extends H/sub /spl infin//-like synthesis techniques to allow for controller dependence on the time-varying plant parameters /spl theta/. The dependence on /spl theta/ is restricted to be linear fractional. The resulting parameter-dependent output feedback problem is reformulated as a robust performance problem with structured uncertainty and solved by elementary state-space manipulations. Feasibility is characterized in terms of linear matrix inequalities which can be solved by convex optimization techniques. Finally a characterization of time-invariant robust controllers is obtained as a special case. >