ON A GENERAL OPTIMAL ALGORITHM FOR MULTIRATE OUTPUT-FEEDBACK CONTROLLERS OF 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 as the extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages between the optimal transient response of LQR control problem and the optimal steady-state noise regulation of SLQR control problem. In general the solution of this algorithm is solved from 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 also discussed. A reducible case is the well-known optimal algorithm derived by AL-Rahmani and Franklin [1], where the system has complete state information, and the discrete-time quadratic performance index is transformed from a continuous-time quadratic performance index.