Robust Linear Quadratic Control of Systems with Integral Quadratic Constraints

In this paper, we consider the robust linear quadratic (LQ) control problem for a class of uncertain linear systems which are subject to a general type of integral quadratic constraints (IQCs). Both analysis and synthesis problems are considered in this paper. For the analysis problem, we determine if the system satisses a desired linear quadratic performance index for all admissible uncertainties subject to the IQCs while for the synthesis problem, we look for a dynamic output regulator to guarantee certain level of performance index. We show that the two addressed problems can be eeectively solved using linear matrix inequalities (LMIs). Some discussions on the optimization of the guaranteed performance index are also included .