Analysis and Design of LTI Full-State Observers: A New Approach to an Old Problem

Eigenvalue-assignment methods for observer designs of linear time invariant (LTI) systems are crucial for both the decaying and the performance characteristics of the observer response. Contrary to the conventional, cumbersome techniques, mainly concentrating on placing individually the observer poles sufficiently far to the left of the plant ones, a novel approach is established that: i) assigns all real parts of the observer eigenvalues at any arbitrary, common for all, predetermined position, ii) provides the region limits and the managing capabilities of modulating the corresponding imaginary parts, iii) results in a very simple procedure by solving a Lyapunov-type equation, for which it is guaranteed that a solution always exists. As is shown by conducting a complete theoretical analysis, the implementation of the proposed method is simple and straightforward, obtaining a stable observer-gain matrix. The latter makes it ideal for designing full-state estimators for LTI systems especially of large or very large dimensions, such the ones met in power applications, etc. This is further demonstrated by applying the technique to a 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup>-order linearized model of a thyristorcontrolled series capacitor (TCSC)-power unit. The proposed approach is thus highlighted and evaluated through the system responses.