Matrix interpolation: some control applications

Matrix interpolation theory has provided a very useful and elegant mathematical tool to analyse the problems which could be translated into some matrix equations. It could also be applied to justify some convenient known results frequently used in many instances. In this paper, a brief review of this theory and some of its applications in control engineering are presented. Solutions of some matrix equations, Pole Placement Problems (PPP) for Multi-Input MultiOutput (MIMO) plants and Model Matching Problem (MMP) are outlined and the results are summarized in step by step algorithms. A new method pro® ting matrix interpolation is introduced for achieving Diagonal Dominance (DD) or almost decoupling of MIMO control plants. In the presented method we use matrix interpolation to reduce the computation order and to build con® dence into some known simulation results obtained from similar methods. It is shown that this method provides considerable advantages compared with other existing methods from the point of computational order, uniqueness of solution and its clarity. Finally, a physical plant is controlled by direct Nyquist procedure using the presented method for achieving DD. Having less complexity than other references, the designed controller strongly satis® es the desired performances.