LQG control for systems with scheduling parameter

We discuss control synthesis through a quadratic performance index for linear stochastic systems with scheduling parameter, which we call LQG control synthesis for systems with scheduling parameter. First, modifying the optimal LQG control synthesis for time-varying systems such that it leads to the causal dependence on the scheduling parameter, we propose a synthesis method based on a Riccati differential inequality and a forward Riccati differential equation. Being suggested by a relation between L² gain control for linear systems with scheduling parameter and that for linear time-varying systems, second, we propose another synthesis method based on two Riccati differential inequalities which correspond to two Riccati differential equations in the optimal LQG control synthesis for time-varying systems. To evaluate performance levels of the synthesized LQG controls, we also discuss some bounding techniques of the quadratic performance index.