Unified approach to linear quadratic regulator with time-scale property

A method for decomposition of unified (continuous/discrete) linear quadratic regulator with two-time-scale property is presented. The composite and the reduced-order controls are formulated in standard unified domain. By appropriate transformations, it is shown that the results of continuous-time and discrete-time obtained previously using two separate techniques, can be obtained by this single unified technique. With this method, there is no need to consider two time-scale systems in continuous and the discrete domains separately. This paper also presents some numerical examples to illustrate the theoretical results.