Singular LQ sub-optimal control problem for a class of discrete-time singular systems with time-delay

Singular linear quadratic (LQ) sub-optimal control problem for a class of discrete-time singular systems with time-delay is investigated. First, based on the algebra equivalent transformation, the original singular LQ problem is transformed into a nonsingular LQ problem for standard discrete-time systems with time-delay. Under some general conditions, the optimal control law of the original LQ problem is given via successive approximation approach. The optimal control law can be synthesized as a sum of state feedback term and a time-delay compensation term which is a limit of a sequence of adjoint vectors.