LQG control design for LPV systems

A parameter-dependent output-feedback control problem is considered. The parameter is assumed to be measurable in real-time, so that the controller can depend causally on its value. The performance objective is the expectation of a quadratic integral cost function. In one case, a Kalman filter based on the time-varying parameter value is implemented in real-time, and a “worst-case” state-feedback controller is designed in place of the optimal regulator. This is necessary since the optimal regulator depends acausally on the system model, which is time-varying and not known a priori in this problem. Another one is to use the solutions of two Riccati inequalities directly. Our paper derives computable bounds on the guaranteed performance for both cases, and proposes an “one-step” scheme to reduce these bounds