SOLVABILITY CRITERION FOR THE CONSTRAINED DISCRETE LYAPUNOV AND RICCATI-EQUATIONS

Conditions for the solvability of the discrete Lyapunov and the discre te Riccati equations subject to linear equality constraints are derive d. These problems arise naturally in the context of output min-max rob ust control. It is shown that the following problems are equivalent to one another: (a) the solvability of the constrained discrete Riccati equation; and (b) the existence of a feedback gain that guarantees the solvability of the constrained discrete Lyapunov equation of the resu lting closed loop. A simple criterion for the existence of a solution to both problems is presented. These problems are shown to be related to the discrete positive real property.