An Algebraic Approach to the Observer-Based Feedback Stabilization of Linear 2D Discrete Models

Abstract

In a recent work, we have investigated the state feedback structural stabilization of linear 2D discrete models. Our main tools are a procedure which enables the state feedback stabilization of Roesser models and equivalence transformations in the sense of the algebraic analysis approach to linear systems theory. Starting from a Fornasini-Marchesini model, we can compute (if it exists) a stabilizing state feedback control law for an equivalent Roesser model and we can then recast it in order to obtain a stabilizing control law that can be applied to the original Fornasini-Marchesini model. Extending the same idea, we here focus on the observer-based dynamic output structural stabilization of linear 2D discrete models within the algebraic analysis framework. Given a Fornasini-Marchesini model, we briefly show how an equivalent Roesser model can be stabilized (if possible) by an observer-based controller computed through existing techniques. Then, we show how to interpret the obtained control law so that it stabilizes the original Fornasini-Marchesini model. Finally, we discuss the cases where our procedure succeeds and we point out some cases where it fails, giving insights to tackle the difficulties encountered in the latter cases.