Singular LQ optimal control for single-input linear digital control systems

The authors discuss the singular LQ optimal control problem for single-input linear digital control systems. The singular LQ control problem can be transformed into the nonsingular one under the reachability condition. The singular LQ optimal controls are obtained for the free-end-point problem, for the fixed-end-point problem, and for the infinite control time problem. They are obtained by state feedback with bounded gains. Furthermore, the relation between the singular LQ optimal control and the nonsingular one is described. For the fixed-end-point problem, the singular LQ optimal control and the nonsingular one can be described by using the same expressions. The infinite control time problem must be regarded as the case when the terminal time approaches infinity in the fixed-end-point problem