The linear-quadratic optimal regulator of time-invariant discrete singular systems

摘要

The LQ linear-quadratic problem of multiple-valued time-invariant discrete singular systems is discussed. The equivalence relation between this problem and that of standard state-space systems is given via an artificial feedback approach under some conditions, and the existence and uniqueness of the optimal control-trajectory pair are obtained. The state feedback synthesis of the optimal control is also derived, and the optimal closed-loop system is single-valued and asymptotically stable.