Fundamental theorem for optimal output feedback problem with quadratic performance criterion

The problem of global optimal static output feedback control for linear time-invariant systems with linear quadratic index in the cases of random initial conditions and deterministic initial conditions was investigated. For the given initial condition (the random case), the necessary and sufficient condition-a matrix equation is obtained for the output feedback control to be equal to the optimal state feedback control and in this case, the output feedback is globally optimal. Further, for the deterministic case, the main contribution is to reveal the dependence of the global optimal feedback gain on the given initial condition. All results are described in a linear algebraic equation.