Adaptation of optimal control theory to systems with time delays

Control of linear time-invariant systems with time delays is considered. Methods for design of both continuous and discrete-time controllers suggested in the literature are discussed and compared in terms of approximations made, generality, implement-ability, and control quality. It is found that for many systems with delays in the state variables, suboptimal control laws give sufficiently good control quality. For systems with delays in the control variables, the control quality is more sensitive to the choice of the controller type. The more sophisticated methods to design control laws in general require large computation time, and therefore methods to reduce the computational burden are discussed. A method found to be suitable in many cases is an extension of a method suggested by Day and Hsia. The extension made in this paper does not concern the method as such but extends the applicability of the method. The methods studied are illustrated through application to two examples by use of digital simulation.