This brief solves some synthesis problems for a class of linear systems for which the state takes nonnegative values whenever the initial conditions are nonnegative. In particular, the synthesis of state-feedback controllers is solved in terms of linear programming problem, including the requirement of positiveness of the controller and its extension to uncertain plants. In addition, the synthesis problem with nonsymmetrical bounds on the stabilizing control is treated

A treatment of the positive observation problem for positive systems is provided, for the continuous and discrete-time cases. The proposed observers are positive, that is, they ensure that the estimates are nonnegative at any time. Moreover, necessary and sufficient conditions for the existence of such positive observers are formulated in terms of linear programming. Also, we show how positive observers can provide guaranteed bounds on the real states of uncertain positive systems. In addition, some implications are discussed; especially, it is shown that it is not possible to stabilise an unstable system using these positive observers. Finally, the applicability of the proposed interval estimation approach is shown for an illustrative application from pharmacokinetics.

This paper provides a new treatment of the theory of positive observers for discrete linear positive systems. The provided conditions for the existence of a positive observer are necessary and sufficient and solvable in terms of linear programming. Unlike the classical theory of observers, we also show that it is no longer possible to stabilize any unstable positive system by using positive observers. Numerical examples are given to show the applicability of the proposed approach

Stabilization problem of positive discrete-time systems with bounds on the inputs or the states is solved in this paper. First, the synthesis of state-feedback controllers that ensure the nonnegativity and the stability of the unconstrained closed-loop systems is studied for both the nominal and uncertain systems. These results are then extended to the case of bounded controls and also for systems with bounds on the states. All the proposed conditions are solvable in terms of Linear Programming. A cost function is then proposed to synthesis controllers with good performance. An example illustrate the feasibility of the proposed approach.

This article deals with sufficient conditions of asymptotic stability for discrete two-dimensional (2D) time switching systems represented by a model of Roesser type with state feedback control. This class of systems can correspond to 2D state space or 2D time space switching systems. This work is based on common and multiple Lyapunov functions. The results are presented in LMI form. Two examples are given to illustrate the results.