STABILIZATION AND OPTIMAL REGULATOR PROBLEM FOR TIME-DELAY SYSTEMS BASED ON THE 2D RICCATI MATRIX EQUATION

Real control objects often include time delays in the path between the input and the output or in the internal signal channel. In such cases , in order to stabilize the system, it is necessary to consider time-d elay systems as a mathematical model of the control object. Expressing the state equation of a time-delay system as a 2D system, we can inve stigate the stability of the closed-loop system by the 2D matrix Lyapu nov equation (MLE). We can also derive the 2D algebraic Riccati equati on (ARE), which gives the delay-independent solution of the optimal re gulator for time-delay systems. If this 2D ARE has a block diagonal po sitive-semidefinite solution, the solution to the optimal regulator fo r time-delay systems is given by the state feedback, and simultaneousl y the value of the linear quadratic cost function becomes a minimum. T he solution to the proposed 2D ARE in this paper can be obtained by th e positive-definite solution to the 1D ARE for discrete-time systems a nd continuous-time systems, with a partial amendment of the weighting matrix of the linear quadratic cost function. (C) 1998 Scripta Technic a.