Abstract
The observation problems for a wide class of discrete-time linear control systems are considered. The problems are to find observability conditions and to design state- and functional-observers. The class of control systems includes systems with multi-inputs and multi-outputs, and systems with singular transient matrices.
First, the k-observability of the dual state of a control system and the observability of a control system are defined, and their necessary and sufficient conditions are obtained. Next, using the k-observability of a dual state, the minimal-time state-observer is defined and a construction of the observer is given. For a kind of nth-order control system with m independent outputs, the observer obtained by the construction has an order less than (n-m)-order. Finally a functional-observer estimating a linear functional of states is derived from the minimal-time state-observer. And it is shown that when k-times observations are necessary to know the value of the functional, then the minimal-order of the functional-observer is equal to k-1.
