A convex characterization of parameter-dependent H∞ controllers

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 θ. 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 θ undergo large variations during system operation. In particular, higher performance can be achieved by control laws which incorporate available measurements of θ and therefore “adjust” to the current plant dynamics. This paper extends H _∞-like synthesis techniques to allow for controller dependence on the time-varying plant parameters θ. The dependence on θ 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