J.M.G. da Silva

Antiwindup design with guaranteed regions of stability: an LMI-based approach

This note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs. Considering that a linear dynamic output feedback has been designed to stabilize the linear system (without saturation), a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed-loop system. It is shown that the closed-loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity. A modified sector condition is then used to obtain stability conditions based on quadratic Lyapunov functions. Differently from previous works these conditions are directly in linear matrix inequality form. Some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones.

Stability analysis and stabilization of systems presenting nested saturations

This note addresses the problems of stability analysis and stabilization of systems presenting nested saturations. Depending on the open-loop stability assumption, the global stability analysis and stabilization problems are considered. In the (local) analysis problem, the objective is the determination of estimates of the basin of attraction of the system. Considering the stabilization problem, the goal is to design a set of gains in order to enlarge the basin of attraction of the closed-loop system. Based on the modelling of the system presenting nested saturations as a linear system with dead-zone nested nonlinearities and the use of a generalized sector condition, linear matrix inequality (LMI) stability conditions are formulated. From these conditions, convex optimization strategies are proposed to solve both problems

Anti-windup design with guaranteed regions of stability: an LMI-based approach

This paper addresses the design of anti-windup gains for obtaining larger regions of stability for linear systems with saturating inputs. Considering that a linear dynamic output feedback has been designed to stabilize the linear system (without saturation), a method is proposed for designing an anti-windup gain that maximizes the estimation of the basin of attraction of the closed-loop system. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system with a deadzone nonlinearity. A modified sector condition is then used to obtain stability conditions based on quadratic Lyapunov functions. Different from previous works, these conditions are directly in LMI form. Several examples illustrate the effectiveness of the proposed design technique when compared with the previous ones.

Evaluation of the genotoxic effect of rutin and quercetin by comet assay and micronucleus test

Flavonoids are phenolic compounds, naturally found in vegetables, tea and red wines. A recent study has demonstrated that the flavonoids rutin and quercetin show a protective role against the deleterious effects of free radicals in cirrhotic rats. Considering this finding and the controversial results concerning the mutagenicity of rutin and quercetin recorded in the literature, the capacity of these flavonoids to cause damage to the DNA was evaluated using the alkaline single-cell gel electrophoresis (SCG) and micronucleus test in the bone marrow of mice. The doses for both compounds were 2 x 2500, 2 x 1250 and 2 x 625 mg/kg. Micronucleus test showed that rutin caused no damage to the DNA of the mice bone marrow cells, and the SCG assay demonstrated an increase of damage only at the dose of 2 x 1250 mg/kg. But when the mice cells of the three quercetin doses were compared with the negative control, significantly higher damage was observed by SCG assay, although not proportional to the dose. The micronucleus test also demonstrated a significant increase of damage, but only at the 2 x 1250 mg/kg dose. Considering the results obtained in this study with very high doses, it is unlikely that the consumption of rutin and quercetin produces any clastogenic effects. Our results also indicated that SCG could profitably be used in drug genotoxicity evaluation protocols.

Polyhedral regions of local stability for linear discrete-time systems with saturating controls

The study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a linear system with an additive disturbance. From this representation, a necessary and sufficient condition relative to the contractivity of a given convex compact polyhedral set is stated. Consequently, the polyhedral set can be associated with a Lyapunov function and the local asymptotic stability of the saturated closed-loop system inside the set is guaranteed. Furthermore, it is shown how, in some particular cases, the compactness condition can be relaxed in order to ensure the asymptotic stability in unbounded polyhedra. Finally, an application of the contractivity conditions is presented in order to determine local asymptotic stability regions for the closed-loop saturated system.

Dynamic Output Feedback for Discrete-Time Systems Under Amplitude and Rate Actuator Constraints

The aim of this work is the proposition of a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. The nonlinear effects introduced by the saturations in the closed-loop system are taken into account by using a generalized sector condition, which allows to propose theoretical conditions to solve the problem directly in the form of linear matrix inequalities (LMIs). From these conditions, convex optimization problems to the determination of the controller in order to address the synthesis requirements are proposed. In addition to the asymptotic stability requirement, two implicit design objectives are considered: the maximization of the region of attraction of the closed-loop system and the guarantee of a certain degree of time-domain performance for the system operation in a neighborhood of the origin (equilibrium point). A numerical example is provided to illustrate the application of the proposed method.

Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances

This paper addresses the problem of synthesis of state feedback control laws for systems subject to /spl Lscr//sub 2/-bounded disturbances in presence of saturating actuators. Conditions that allow to guarantee both the internal and external stability of the closed-loop system are proposed. They are formulated from the use of the Finslers lemma and a generalized sector non-linearity description. This approach allows to introduce new variables (multipliers) in the problem which increase the degrees of freedom in the synthesis problem. Based on the stability conditions, a multiobjective problem is addressed: the synthesis of a state feedback gain that simultaneously maximizes the magnitude of the admissible /spl Lscr//sub 2/-disturbance and the size of the domain of stability of the closed-loop system.

Estimating the Region of Attraction of Nonlinear Control Systems with Saturating Actuators

This paper focus on the problem of estimating the region of attraction of nonlinear control systems that can be put in a rational algebraic-differential form. The estimates are computed by means of invariant domains associated to rational Lyapunov functions. The saturation effects are taken into account by the use of a generalized sector condition for deadzone nonlinearities. These ingredients lead to the formulation of an LMI-optimization problem for computing regions of stability for the closed-loop system.

Repetitive Control Design for MIMO Systems With Saturating Actuators

This paper addresses the problem of tracking and rejection of periodic signals for linear multi-input, multi-output systems subject to control saturation. To ensure the periodic tracking/rejection, a modified state-space repetitive control structure is considered. Conditions in a “quasi” linear matrix inequality form are proposed to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Provided that the references and disturbances belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain ellipsoidal set contract to the linearity region of the closed-loop system, where the presence of the repetitive controller ensures the periodic tracking/rejection.

Correction to "Antiwindup Design With Guaranteed Regions of Stability: An LMI-Based Approach"

In the footnote of J.M. Gomes da Silva, Jr. and S. Tarbouriech (see ibid., vol.50, no.1, p.110, 2005), we have stated that the value of 61.29 obtained by Y.Y. Cao et al. (2002) was apparently incorrect. In fact, the different values come from the fact that the example considered by Y.Y. Cao is slightly different from the one by J.M. Gomes da Silva, Jr. and S. Tarbouriech (2005). Hence, the result presented by Y.Y. Cao is indeed correct and we apologize to the authors for the misunderstanding.