DARE solutions for LQ optimal and suboptimal control of systems with multiple input-output delays

The central issue in linear-quadratic (LQ) optimal control problems is finding a solution to Riccati equation. In this paper, infinite-horizon LQ problem and the associated discrete-time matrix algebraic Riccati equation (DARE) for systems involving multiple input-output delays are investigated. The optimal solution is established for appropriately chosen extended state-space system representation. Using structural properties of the considered class of systems, a simplified solution procedure is proposed by direct manipulation of DARE. The order of design equations in the simplified procedure is reduced to that of the undelayed system part. The obtained suboptimal control is shown optimal for a closely related system of delay compensation variables. The control system robustness is examined analytically and verified in numerical tests. The suboptimal control is not only easier to implement but also occurs less sensitive to modeling errors and external perturbations than the optimal strategy.