Linear quadratic Gaussian control of 2-dimensional systems

The linear quadratic Gaussian (LQG) control for one-dimensional (1-D) systems has been known to be one of the fundamental and significant methods in linear system theory. However, the LQG control problem for two-dimensional (2-D) systems has not been satisfactorily solved due to their structural and dynamical complexity. In this paper, sufficient conditions for evaluation of the quadratic performance indices of 2-D systems in terms of the system state and control variables are proposed. Using these conditions, systematic design methods for finite horizon and infinite horizon LQG controls of 2-D systems are developed.