A unified approach to LMI-based reduced order self-scheduling control synthesis

We consider a reduced order controller synthesis for a general class of control specifications for linear parameter-varying (LPV) systems, when some of state variables are exactly available. The class is defined in an abstract manner so that it uniformly deals with many significant specifications. A necessary and sufficient condition for the existence of a reduced order controller is given in terms of linear matrix inequalities (LMIs). We also show that the order of the controller can be reduced by the number of the state variables exactly available in the measurements. Moreover, in the case of linear time invariant (LTI) systems, a parameterization of all desirable reduced order LTI controllers is given by means of solutions of LMIs. The results in this paper generalize the class of control specifications in which a reduced order controller exists, making it possible to synthesize a reduced order controller based on LMIs for multi-objective control specifications. Furthermore, these results uniformly describe and generalize the existing results on synthesis of a constant state and a full order output feedback controller for LTI and LPV systems such that the specification is given by the existence of a constant positive definite matrix.