A Design Method of Pole Placement and Observer for Non-Lexicographically-Fixed Linear Time-Varying Discrete MIMO Systems

Abstract

The linear time-varying multivariable system whose controllability indices or observability indices are not constant is called the non-lexicographically-fixed system. Valasek proposed the pole placement design method for such a continuous system by augmenting the system equation so that the augmented system is lexicographically-fixed. This paper concerns the pole placement and the observer design method for linear time-varying discrete non-lexicographically-fixed system. Using the Valasek's idea, the procedure to augment a discrete non-lexicographically-fixed system to a lexicographically-fixed augmented system will be presented. Then, the simple pole placement technique can be applied to the augmented system without transforming the system into any canonical form. Further, using the property of the anti-causal dual system, it will be shown that the pole placement design method can be used for the augmented observer for non-lexicographically-fixed systems. Finally, the stability and the separation principle of the total closed loop system are also shown for the case where both of the augmented pole placement controller and the augmented observer are used.