Abstract: This paper proposes an optimal control design method for a class of discrete-time nonlinear time-delay systems, subject to mixed control-state constraints. The delays in the systems are in state and/or in control input. An optimal control is designed based on the measure theory, functional analysis and linear programming by optimising a definite objective function and transferring the difference system equation into a new metric space in which the number of the sample times are the same but their values and properties may differ. In fact, by an embedding process the problem is nearly the same as in a continuous case. The problem is first transferred to a new optimal measure problem and then this new problem is replaced with one in which minimising a linear form over a subset of linear equalities is required. It is shown that this minimisation is global and the embedding procedure allows one to develop a computational method to find a solution using a finite–dimensional linear programming problem. A numerical example is also presented to illustrate the procedure of the method. .

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