On a general optimal algorithm for multirate output feedbackcontrollers for linear stochastic periodic systems

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one