Controller synthesis for positive 2D systems described by the Roesser model

Abstract

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.

Linear Programming Approach for 2-D Stabilization and Positivity

“…Using a simple convexity property, the LP formulation proposed in Theorem 2 can be easily extended to these systems with polytopic uncertainties, by just repeating the LP conditions for all the vertices in the polytope, using similar ideas as those proposed by some of the authors in [11], as stated in the following result.…”

“…In the present paper, we first analyze the stability of linear positive 2-D models [7], following ideas borrowed from 1-D systems [1], already used by some of the authors for Roesser models [11], deriving a necessary and sufficient condition for 2-D stability, based on simple linear inequalities. From this result, a simple numerical method is proposed for a complete treatment of the stabilization problem of these positive 2-D systems, when they can be described by a Fornasini-Marchesini second model (A parallel result for Roesser 2-D systems is presented in [2]).…”

Control Synthesis for General Positive 2D Models

“…The stability of 2D positive systems described by Roesser model and synthesis of state-feedback controllers has been considered in [10], some other results of sufficient conditions for asymptotic stability and stabilization problem for 2D discrete linear systems can be found in the literature [11] and some recent results [5][6][7][8]12].…”

Asymptotic stability of positive 2D linear systems with delays

“…The stability of 2D positive systems described by the Roesser model and synthesis of state-feedback controllers have been considered in the paper [20]. The asymptotic stability of positive 2D linear systems has been investigated in [21].…”