Sophie Tarbouriech

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

Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach

Deals with the problem of local stabilization of linear discrete-time systems subject to control saturation. A linear matrix inequalities-based framework is proposed in order to compute a saturating state feedback that stabilizes the system with respect to a given set of admissible initial states and, in addition, guarantees some dynamical performances when the system operates in the zone of linear behavior (i.e., when the controls are not saturated).

Synthesis of controllers for continuous-time delay systems with saturating controls via LMIs

The stabilization of linear continuous-time systems with time delay in the state and subject to saturating controls is addressed. Sufficient conditions obtained via a linear matrix inequality (LMI) formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements. The method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed-loop system is guaranteed when control saturations effectively occur.

Finite-Time Stabilization of Linear Time-Varying Continuous Systems

In this technical note, the problem of finite time stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach.

Stability regions for linear systems with saturating controls via circle and Popov criteria

The problem of local stabilization of linear continuous-time systems subject to input saturation is addressed. The determination of stability regions for the saturated system is first considered via both the circle and Popov criteria. The absolute stability with a finite domain is thus studied from the resolution of some Riccati equations and quadratic optimization problems under linear constraints. Next, the synthesis of both state feedback controllers and stability domains is proposed via the use of linear matrix inequalities.

A Tutorial on Modern Anti-Windup Design

In this paper, several constructive linear and nonlinear anti-windup techniques are presented and explained. Two approaches, namely direct linear anti-windup (DLAW) and model recovery anti-windup (MRAW), are described in an algorithmic way, in order to illustrate their main features. Hereafter, theoretical conditions ensuring stability and performance, their applicability, their accompanying guarantees, and their merits and deficiencies are given. The possible extensions to less standard problem settings are also briefly discussed.

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.

Advanced Strategies in Control Systems with Input and Output Constraints

Anti-windup Augmentation for Plasma Vertical Stabilization in the DIII-D Tokamak.- Stable and Unstable Systems with Amplitude and Rate Saturation.- An Anti-windup Design for Linear Systems with Imprecise Knowledge of the Actuator Input Output Characteristics.- Design and Analysis of Override Control for Exponentially Unstable Systems with Input Saturations.- Anti-windup Compensation using a Decoupling Architecture.- Anti-Windup Strategy for Systems Subject to Actuator and Sensor Saturations.- Sampled-Data Nonlinear Model Predictive Control for Constrained Continuous Time Systems.- Explicit Model Predictive Control.- Constrained Control Using Model Predictive Control.- Risk Adjusted Receding Horizon Control of Constrained Linear Parameter Varying Systems.- Case Studies on the Control of Input-Constrained Linear Plants Via Output Feedback Containing an Internal Deadzone Loop.- Set Based Control Synthesis for State and Velocity Constrained Systems.- Output Feedback for Discrete-Time Systems with Amplitude and Rate Constrained Actuators.- Decentralized Stabilization of Linear Time Invariant Systems Subject to Actuator Saturation.- On the Stabilization of Linear Discrete-Time Delay Systems Subject to Input Saturation.

Brief paper: Control design for a class of nonlinear continuous-time systems

This paper addresses the control design problem for a certain class of continuous-time nonlinear systems subject to actuator saturations. The system under consideration consists of a system with two nested nonlinearities of different type: saturation nonlinearity and cone-bounded nonlinearity. The control law investigated for stabilization purposes depends on both the state and the cone-bounded nonlinearity. Constructive conditions based on LMIs are then provided to ensure the regional or global stability of the system. Different points, like other approaches issued from the literature, are quickly discussed. An illustrative example allows to show the interest of the approach proposed. c 2008 Elsevier Ltd. All rights reserved.