A geometric theory for 2-D systems including notions of stabilisability

In this paper we consider the problem of internally and externally stabilising controlled invariant and output-nulling subspaces for two-dimensional (2-D) Fornasini–Marchesini models, via static feedback. A numerically tractable procedure for computing a stabilising feedback matrix is developed via linear matrix inequality techniques. This is subsequently applied to solve, for the first time, various 2-D disturbance decoupling problems subject to a closed-loop stability constraint

Detectability subspaces and observer synthesis for two-dimensional systems

The notions of input-containing and detectability subspaces are developed within the context of observer synthesis for two-dimensional (2-D) Fornasini-Marchesini models. Specifically, the paper considers observers which asymptotically estimate the local state, in the sense that the error tends to zero as the reconstructed local state evolves away from possibly mismatched boundary values, modulo a detectability subspace. Ultimately, the synthesis of such observers in the absence of explicit input information is addressed

Linear Algebra Methods for the Control of Multidimensional Systems

The purpose of the thesis is to develop a comprehensive theory of the geometric control for N-dimensional systems. Two possible representations and their structural invariance properties of 2-D systems will be considered and generalised to the N-dimensional case: the Fornasini-Marchesini first order model and Fornasini-Marchesini second order model. In addition, necessary and sufficient conditions for the existence of solutions for the implicit 2-D Fornasini-Marchesini models will be provided, and generalised to the N-dimensional case

Self-boundedness and self-hiddenness for implicit two-dimensional systems

In this paper we introduce and develop the concepts of self-boundedness and self-hiddenness for implicit two-dimensional systems. The aim of this note is to show that when extending such concepts to a multidimensional setting, a richer structure arises than in the one-dimensional case