Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.
This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov-Krasovski functional combined with Finsler's lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.
This paper deals with the stability synthesis for a class of 2D linear systems described by the Roesser model. We provide necessary and sufficient conditions for stability, as well as stabilization for linear positive Roesser systems. This kind of systems have the property that the states take nonnegative values whenever the initial boundaries are nonnegative. The synthesis of state-feedback controllers, including the requirement of positivity of the controllers and the extension of the results to uncertain plants are solved in terms of Linear Programming. A numerical example is included to illustrate the proposed approach.
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