Observer Design for Large-Scale Linear Systems

This paper presents an approach which reduces the computational requirements in observer design. Specifically, a procedure is developed which reduces the observer design to an algebraic problem of solving an (n- 2m)X(n-m) matrix equation, where n is the dimension of the state and m is the dimension of the output It is also shown that for a special class of problems, which appears very often in time-series modeling, the computational requirements can be much further reduced. The procedure developed in this paper is applicable to both Discrete-Time and continuous-time linear dynamic systems. The resulting observer will have m eigenvalues clustered together at a selected point and the remaining n – 2m eigenvalues are arbitrarily placed.