Stability and stabilisation of 2D discrete linear systems with multiple delays

In this paper, we study the stability and the stabilisation of 2D discrete linear systems with multiple state delays. All of the new results obtained are based on analysis of the Fornasini-Marchesini state space model with delays and the resulting conditions are given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the overall approach.published_or_final_versio

Measurements, Models, Systems and Design

531 s.

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

Multidimensional Systems

W pracy zawarty jest rys historyczny oraz przegląd podstawowych problemów teoretycznych i możliwości zastosowania praktycznych układów wielowymiarowych (nD). Omówiono też nowe trendy i otwarte, nierozwiązane do tej pory problemy badawcze w tej dziedzinie.The history, theoretical basics and practical applications of multidimensional (nD) systems are briefly revisited. New directions and current open problems are discussed too

Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Repetitive processes propagate information in two independent directions where the duration of one of these is infinite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops robust controller design algorithms for discrete linear processes based on the poly-quadratic stability that produce less conservative results than currently available alternatives