Fernando Tadeo

Controller Synthesis for Positive Linear Systems With Bounded Controls

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

Control of constrained positive discrete systems

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.

Positive observation problem for linear time-delay positive systems

This paper deals with the problem of positive observation for linear time-delay systems for which the states take nonnegative values whenever the initial conditions are nonnegative. We focus on the design of positive observers (possibly with time-delay) which guarantee nonnegative estimates of the current states. We derive necessary and sufficient conditions for the existence of a positive observer (extended Luemberger-type) and show that the solvability of the problem can be decided via standard linear programming techniques. Moreover, on the negative side, it is shown that one cannot stabilize any unstable positive time-delay system by using extended Luenberger type positive observers. In other words, the separation principle does not hold.

Regulator problem for linear systems with constraints on control and its increment or rate

This paper discusses the problem of constraints on both control and its rate or increment, for linear systems in state space form, in both the continuous and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate (for the continuous-time case), such that the system evolves respecting incremental or rate constraints. A pole assignment technique is then used to solve the inverse problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on both control and its increment or rate. An illustrative example shows the application of the method on the double integrator problem.

LMI-Based Approach for Output-Feedback Stabilization for Discrete-Time Takagi--Sugeno Systems

This paper presents a static output-feedback stabilizing controller design for nonlinear systems represented by discrete-time Takagi-Sugeno fuzzy models. The main result concerns the stabilization based on the parallel distributed compensation (PDC) approach. Sufficient conditions are provided for quadratic and nonquadratic stabilization. A numerical procedure based on the cone complementarity algorithm is given for the design of static output-feedback stabilizing controller. It is shown that the relaxed conditions proposed in the nonquadratic case outperform those for the quadratic case. A numerical example is given to illustrate the applicability of the proposed approach

Positive observers for linear positive systems, and their implications

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.

Robust Exact Pole Placement via an LMI-Based Algorithm

This technical note deals with the robust exact pole placement problem: pole placement algorithms that guarantee a small variation of the assigned poles against possible perturbations. The solution to this problem is related to the solvability of a Sylvester-like equation. Thus, the main issue is to compute a well-conditioned solution to this equation. Also, the best candidate solution must possess the minimal condition number, to reduce sensitivity to perturbation. This problem is cast as a global optimization under linear matrix inequality constraints, for which a numerical convergent algorithm is provided and compared with the most attractive methods in the literature.

The Regulator Problem for Linear Systems With Saturations on the Control and its Increments or Rate: An LMI Approach

This paper solves the problem of designing stabilizing regulators for linear systems subject to control saturations and asymmetric constraints on its increment or rate, using reduced dimension linear matrix inequalities (LMIs) developed on a reduced-order state space. Compared with previous approaches, the proposed technique is valid for asymmetric constraints on the increment or rate of the control while the computing time is improved by resolving LMIs of reduced dimensions

Robust H_{\infty } filtering for uncertain two-dimensional continuous systems with time-varying delays

This paper deals with the problem of delay-dependent robust