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International audience; This paper investigates an event-triggered control design approach for discrete-time linear parametervarying (LPV) systems under control constraints. The proposed conditions can simultaneously design a parameter-dependent dynamic output feedback controller and an event generator, ensuring the closedloop system's regional asymptotic stability. Based on the Lyapunov stability theory, these conditions are given in terms of linear matrix inequalities (LMIs). Moreover, using some proposed optimization procedures, it is possible to minimize the number of sensor transmissions, maximize the estimation of the region of attraction of the origin, and incorporate optimal control criteria into the formulation. Through numerical examples, some comparisons with other approaches in the literature evidence the proposed technique's efficacy.

In this paper, we focus on the “positive” l 2 induced norm of discrete-time linear time-invariant systems where the input signals are restricted to be nonnegative. To cope with the nonnegativity of the input signals, we employ copositive programming as the mathematical tool for the analysis. Then, by applying an inner approximation to the copositive cone, we derive numerically tractable semidefinite programming problems for the upper and lower bound computation of the “positive” l 2 induced norm. This norm is typically useful for the stability analysis of feedback systems constructed from an LTI system and nonlinearities where the nonlinear elements provide only nonnegative signals. As a concrete example, we illustrate the usefulness of the “positive” l 2 induced norm for the stability analysis of recurrent neural networks with activation functions being rectified linear units.

Cette communication devait être présentée au congrès "24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020)" qui a été annulé. Reporté en 2021; International audience; This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The novelty of the proposal relies on the use of an anti-windup loop to drive the state of the allocator, which in some sense dynamically compensates the difference between the computed control signal and the plant input. Furthermore, the co-design of the allocator and anti-windup loop is presented, allowing to deal with the multiple objective of reducing the allocator error and increasing the closed-loop region of stability. Theoretical conditions are derived in terms of linear matrix inequalities (LMIs) and an optimization scheme consisting in the minimization of the energy of the allocator error is proposed. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.

This work deals with the problem of designing stabilizing event-triggered state-feedback controllers for rational systems. Using differential algebraic representations and Lyapunov theory techniques, LMI-based conditions are derived to ensure regional asymptotic stability of the origin. These conditions are then cast into a convex optimization problem to the co-design of the event generator parameters and the state-feedback gain in order to reduce the controller updates while ensuring the asymptotic stability of the origin with respect to a given set of admissible initial conditions. The proposed methodology is illustrated by means of a numerical example.

This paper deals with design methods of event-triggered control systems for discrete-time linear systems. An extended plant consisting of a given plant and a dynamical filter is considered and controlled by an event-triggered static output feedback. The triggering rule uses only the available signals and therefore is based on the difference between the triggered and non-triggered output signals. The paper deals with the co-design problem, that is the design of the triggering condition, the filter, and the controller simultaneously. Sufficient theoretical conditions are proposed in terms of linear matrix inequalities to ensure the asymptotic stability of the closed-loop system. Convex optimizations problems incorporate these conditions in order to optimize the closed-loop performance or to reduce the number of transmissions. Three numerical examples illustrate the design method of the triggering conditions as well as the simultaneous design method of the filter and controller.

The paper addresses the design of an event-triggering mechanism for a partial differential wave equation posed in a bounded domain. The wave equation is supposed to be controlled through a classical damping term: the first order time derivative of the solution, distributed in the whole domain. In a continuous framework, such a feedback leads to the global exponential stability of the closed-loop system. Here, sufficient conditions based on the use of a suitable Lyapunov functional are proposed to guarantee that an event-triggered distributed damping ensures the exponential stability. Moreover, the designed event-triggering mechanism allows avoiding the Zeno behavior. The ‘existence and regularity’ prerequisite properties of solutions for the closed loop system are also proven.

The nonlinear action of hybrid PI controllers makes possible to achieve almost none overshot with the smallest rise time possible (for the available input energy) and a settling time almost equal to the rise time. However, all of these nice properties require changes on the control loop. Our contribution is the proposition of a plug-in control action that can be added to the classical linear PI to avoid changes in the hardware, and still achieve the same behavior of a recently introduced adaptive hybrid PI controller. Our proposal is illustrated by real-time level control experiments in a nonlinear reservoir. Performance indexes are presented to evaluate the experimental tests.

This paper deals with a systematic way to check if a certain class of nonlinear systems can define a contraction. The proposed approach combines the use of sector bound condition or monotonic condition satisfied by the nonlinearities with the use of an adequate control function matrix. The contraction analysis results are provided under the form of linear matrix inequalities (LMIs). The design of a nonlinear control law (that is a control law depending on nonlinearities) is proposed in order for the closed loop to be a contraction. The adaptation of the contraction results to the synchronization of n identical nonlinear systems is also investigated by considering two kinds of communication graphs (full and general undirected ones).

The paper presents an observer-based event-triggered control strategy for linear systems subject to input cone-bounded nonlinearities by using only available measurable variables. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop and the avoidance of Zeno behavior in an emulation context. Based on these conditions, a convex optimization problem to compute the parameters of the event-trigger rule aiming at reducing the number of control updates is proposed. The approach is illustrated on a numerical example that considers the control of a linear system with a logarithmic input quantization constraint.

International audience; This article investigates the asymptotic stability of impulsive delay dynamical systems (IDDS) by using the Lyapunov-Krasovskii method and looped-functionals. The proposed conditions reduce the conservatism of the results found in the literature by allowing the functionals to grow during both the continuous dynamics and the discrete dynamics. Sufficient conditions for asymptotic stability in the form of linear matrix inequalities (LMI) are provided for the case of impulsive delay dynamical systems with linear and time-invariant (LTI) base systems (non-impulsive actions). Several numerical examples illustrate the effectiveness of the method.

International audience; Set theory and invariant sets are the key ingredients used in this paper to address the control problem of general anesthesia. The paper is dedicated to adapt such tools in order to validate the multi-phase control law used in practice from the induction phase corresponding to the administration of an open-loop bolus dose to the maintenance phase of the depth of hypnosis during the surgical operation.

This work presents results on the stability of time-delay reset control systems under time-dependent resetting conditions. The stability of a reset control system composed by a time-delay process and a proportional and integrative plus Clegg integrator (PI+CI) compensator is tackled by using the framework of sampled-data systems. It leads to sufficient stability conditions expressed in terms of LMIs (Linear Matrix Inequality), that depend explicitly on the reset times. In contrast to previous results, the proposed conditions allow to guarantee the stability of reset systems with unstable base system.

The problem of ℋ ∞ filter design for continuous-time nonlinear polynomial systems is addressed in this paper. The aim is to design a full order dynamic filter that depends polynomially on the filter states. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an ℋ ∞ performance bound for the augmented polynomial system, composed by the original system and the filter to be designed, in a regional (local) context. Then, by using Finsler’s lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices in the conditions. Imposing structural constraints to the decision variables and fixing some values for a scalar parameter, design conditions for the ℋ ∞ filter can be obtained in terms of linear matrix inequalities. As illustrated by numerical experiments, the proposed conditions can improve the ℋ ∞ performance provided by standard linear filtering by including the polynomial terms in the filter dynamics.

International audience; We construct hybrid loops that augment continuous-time control systems. We consider a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time state feedback controller. The arising hybrid closed loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the closed-loop state space to guarantee that a positive definite function $V$ of the closed-loop state and/or a positive definite function $V_p$ of the plant-only state is non-increasing along the hybrid trajectories. Sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions. For the linear case we illustrate specific choices of the functions $V$ and $V_p$ which allow for the reduction of the overshoot of a scalar output. The proposed approaches are illustrated on linear and nonlinear examples.

The two degrees of freedom parallel robot Par2 is designed for high-speed and high-accuracy industrial pick-and-place operation tasks. As a result of high acceleration trajectories, its end-effector undergoes some undesirable vibrations after reaching the stop position, compromising precision and leading to an increase in the operation cycle time. Accelerometer sensors placed on the end-effector and piezoelectric patch actuators wrapped around the robot arms are employed in order to actively reduce these vibrations. Without taking into account saturation limitations, a robust controller is designed, minimizing vibrations for the robot nominal operating point but failing for some extreme operating points, due to high control efforts. An anti-windup strategy is then employed to deal with the saturation of the actuator. Such a strategy presents the advantage, with respect to the strategy which would consider a controller with smoother control efforts, to maintain a good level of vibration attenuation on the whole operation domain. Simulations and experimental results attest the adequacy of the proposed solution.

The main objective in this paper is to investigate the robust performance degradation for a class of nonlinear systems due to some dynamics that are not taken into account during the controller design stage. This is usually the case in practical applications where a simplified (nonlinear) model is used to design the controller. Therefore, it is expected some performance degradation in the application of such a controller due to the presence of the neglected dynamics. With this purpose, some convex conditions for stability analysis and energy-peak evaluation of nonlinear control systems are given. It is supposed that the nonlinear functions present in the model are subject to bounded uncertainties and that both the simplified model and the neglected dynamics model are affected by polytopic uncertainties. The theoretical conditions providing stability and energy-peak bound on the regulated output of the system despite the presence of uncertainties associated with the nonlinear functions are obtained by means of a parameter dependent Lyapunov function. The proposal is illustrated by numerical examples.

This paper is concerned with the problem of H∞ filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic fi lter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H∞ performance bound for the augmented quadratic system, composed by the original system and the filter to be designed, in a regional (local) context. Then , by using the Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices. Imposing structural constraints to the decision variables , theoretical conditions, which can be treated as linear matrix inequality conditions by fixing a grid on a sc alar parameter, can be derived for the filter design. As illustrated by numerical experiments, the proposed conditions can improve the H∞ performance provided by linear filters by including the quad ratic terms in the filter dynamics.

A procedure to synthesize stabilizing controllers for linear time-varying periodic continuous-time systems is proposed in this paper. The controller is a periodic state-feedback gain whose construction is based on the utilization of the transition matrix of the open-loop system, and the stability of the closed-loop system is guaranteed if the system is controllable and if a observability-based condition is satisfied. The periodic state feedback gain is obtained through the numerical integration of two differential matrix equations over two periods, being the resolution of such equations considerably simpler and computationally more viable than the resolution of Ricatti differential equations considered in the standard LQR approach. Some examples illustrates the validity of the technique.

The paper addresses two control problems of discrete-time switching systems subject to modal nonlinearities satisfying sector conditions, actuator saturations and additive L 2 -bounded disturbances. Such switching systems consist of a finite family of discrete-time processes that are supervised by logical decision-making algorithms. Conditions based on LMIs are provided for synthesizing the control gains and for obtaining regions of absolute λ -contractivity as large as possible or for obtaining a L 2 -gain as small as possible. A numerical example illustrates the proposed approaches.

This paper deals with ultimate bounded stability analysis and stabilization conditions for systems involving input saturation and quantized control law, which corresponds to the state quantization case. The state feedback control design problem is then addressed. Theoretical results to ensure the ultimate boundedness and the L 2 stability of the closed-loop system are presented both in local as well as global contexts. The saturation and quantized nonlinearities are tackled through the use of some modified sector conditions. The proposed conditions are then cast in convex optimization problems aiming at maximizing the region of attraction of the closed-loop system and minimizing the set in which the closed-loop trajectories are ultimately bounded, maximizing the bound of admissible L 2 disturbances or maximizing the L 2 -gain from the disturbance to the regulated output.

This paper focuses on the problem of static anti-windup design for a class of nonlinear systems subject to actuator saturation. Considering that a nonlinear dynamic output feedback controller has been designed to stabilize the nonlinear system, a method is proposed to compute a static anti-windup gain which ensures the local stability of the the closed-loop system while providing an estimate of the region of attraction. The results are based on a differential-algebraic representation of rational systems and a modified sector bound condition to deal with the saturation effects. From these elements, LMI based conditions are proposed to compute an anti-windup gain for enlarging the size of the closed-loop region of attraction. A numerical example is given to illustrate the proposed method.

This paper addresses the problem of stability analysis for a given class of nonlinear systems resulting from the connection of a linear system with an isolated backlash operator. Constructive conditions based on LMIs to ensure closed-loop stability are proposed by using some suitable Lyapunov functionals with quadratic terms and Lure type terms, and generalized sector conditions. Additionally, the boundary of the associated set of all the admissible equilibrium points is precisely defined.

As an original alternative to dynamic inversion techniques, a non-standard anti-windup control strategy is developed in this paper in order to improve the on-ground control system of a civilian aircraft. Using a linear fractional representation (LFR) of the aircraft in combination with an original approximation of the nonlinear ground forces by saturation-type nonlinearities, the proposed design method delivers low-order and robust controllers, which are automatically adapted to the runway state and to the aircraft longitudinal velocity. The efficiency of the design scheme is assessed by several nonlinear simulations.

This paper proposes an anti-windup design technique for systems which contain two sources of nonlinearity, namely actuator saturation and a quadratic nonlinearity in the plant state equation. It is shown how a nominal nonlinear dynamic inversion controller can be augmented with an anti-windup compensator of a form similar to that which is popular in linear anti-windup compensation. It is shown further how the free parameters of this compensator can be chosen, using linear matrix inequalities, in a way in which the region of attraction of the closed-loop compensated system is enlarged. A numerical example illustrates the effectiveness of the proposed technique.

For a class of reset control systems, we reconsider the piecewise quadratic Lyapunov function construction proposed in Zaccarian et al. [2005]. In particular, we propose an alternative construction that addresses an analysis subtlety overlooked in that preliminary result. An example illustrates the potential pitfalls of ignoring this analysis subtlety. Another example is used to show that the new statement leads to numerical results that are similar to the ones that come from Zaccarian et al. [2005].

We construct hybrid loops that augment continuous time control systems consisting in a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time controller. In particular, the arising hybrid closed-loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the closed-loop state space to guarantee that a positive definite function V of the closed-loop state and/or a positive definite function Vp of the plant-only state is non-increasing along the hybrid trajectories. Sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions. The proposed approach is illustrated on a linear and a nonlinear example.

Based on a recent description of deadzone nonlinearities via local sector conditions, a new LMI characterization is proposed in this paper to compute static and full- or fixed-order anti-windup compensators for possibly open-loop unstable plants. The originality of this approach rests on the use of a specific performance criterion which is inspired by the L 2 framework. A significant part of the paper is then devoted to a challenging control problem which involves both magnitude and rate limitations. As an important point in this illustrative part, implementation and robustness issues of the anti-windup device are thoroughly discussed.

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.

This paper addresses the problem of stability analysis for a certain class of nonlinear systems resulting from a sandwiched backlash operator in the connection of a plant and a nonlinear actuator device. The actuator is subject to both amplitude and dynamics saturations. Constructive conditions based on LMIs to ensure the stability of the sandwich system are proposed by using some suitable Lyapunov functionals and generalized sector conditions. The associate set of all the admissible equilibrium points is precisely defined.

New developments on anti-windup synthesis are proposed in this paper. These are based on a recent work on a practical approach to stability and performance analysis of saturated linear systems. Basically, via LMI optimization, the anti-windup gains are calculated so as to minimize a performance index in the nonlinear domain, i.e when saturations are active. Then, a significant part of the paper is devoted to a thorough application, where the relevance of the proposed technique is clearly demonstrated.

Using a recent description of deadzone-type nonlinearities via modified sector conditions, a new LMI characterization of full-order continuous-time anti-windup controllers is first proposed. The reduced-order case is then considered. Here, convexity is lost but can be recovered as soon as the poles of the anti-windup controller are fixed. Based on this result, a two-step design procedure is then implemented in the applicative part of the paper. By convex optimization, the first step consists of designing a full-order anti-windup controller. Then, in the second step, the poles of this full-order controller are analyzed and a selection is made. This selection is finally used to fix the poles of the reduced-order controller, which is easily computed as the solution of an LMI problem. The proposed methodology is evaluated on a real-world application, which reveals that the reduced controller – from which slow dynamics have been removed – even performs better than the full-order one.

In this paper, the problem of practical 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.

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.

This paper focuses on the study and the characterization of stability regions for linear systems with delayed states and subject to input saturation through anti-windup strategies. In particular, the synthesis of anti-windup gains in order to guarantee the stability of the closedloop system for a region of admissible initial states as large as possible is addressed. Based on the modeling of the closed-loop system, resulting from the controller plus the anti-windup loop, as a linear time-delay system with a deadzone nonlinearity, stability conditions in an LMI form are stated, for both the delay independent and delay dependent contexts, by using quadratic functionals and a modified sector condition. LMI-based optimization schemes for computing the anti-windup gains that lead to the maximization of the size of the region of stability associated to the closed-loop system are then proposed. The application of the technique and the trade-off between the size of the delay and the region of stability are illustrated by means of numerical examples.

This paper deals with the synthesis of dynamic anti-windup compensators for discrete-time linear systems with saturating controls. Considering that the system is subject to the action of L2 bounded disturbances, two approaches for computing the antiwindup compensator in order to guarantee both that the systems trajectories are bounded and a certain L2 performance level is achieved by the regulated outputs are proposed. The first approach considers the synthesis of full order compensators and the second one addresses the synthesis of reduced order compensators.

Conditions for existence of observer-based faults detection and isolation systems for continuous linear descriptor systems are presented. These conditions are associated, in a first phase, to the solution of a generalized Sylvester equation and, in a second phase, to the solution of a Sylvester equation under a constraint that describes the faults decoupling of the corresponding estimation error. Two observer structures are used to residual generation and faults reconstruction/isolation, respectively. The proposed results put in evidence some degrees of freedom that can be used for design purposes. Thus, an eigenstructure assignment algorithm to design the FDI system and a illustrative example are presented.

This paper addresses the problem of stability analysis for a certain class of nonlinear systems resulting from a sandwiched backlash operator in the connection of a plant and an actuator device. Constructive conditions based on LMIs to ensure the stability of the sandwich system are proposed by using some suitable Lyapunov functions and generalized sector conditions. The associated set of all the admissible equilibrium points is precisely defined. Extensions to the case where some parameters of the backlash nonlinearity are uncertain are provided.

Linear matrix inequality (LMI) conditions are given for the computation of H ∞ guaranteed costs for neutral systems with time-varying delay in the state vector. All the system matrices are supposed to be uncertain and time-invariant, belonging to a polytope with known vertices. The H ∞ guaranteed costs are assured by means of a parameter- dependent Lyapunov-Krasovskii functional providing less conservative results than those available in the literature in the context of delay independent conditions. LMI conditions for special cases such as delay free systems and retarded systems with time-varying delays can be obtained from the proposed conditions by congruence transformations.

Based on some recent results in regional stability analysis of saturated linear systems, the focus of this paper is to extend the notion of stability to that of performance in a practical way. To this purpose an original method, inspired by the H 2 framework is presented. The effectiveness of our approach is demonstrated on a real-world - open-loop unstable - fighter aircraft example combining both amplitude and rate saturations.

This paper deals with the synthesis of static anti-windup compensators for linear systems presenting both state time-varying delays and saturating inputs. Considering that the system is subject to the action of L 2 bounded disturbances, a method for computing the anti-windup compensator in order to guarantee both that the trajectories of the system are bounded and a certain L 2 performance level is achieved by the regulated outputs, is proposed. Based on Lyapunov-Krazovskii functionals, a descriptor approach and the use of a modified sector-based relation, conditions to solve the problem are derived. From these conditions, LMI-based optimization problems are proposed in order to minimize the L 2 gain, as well as in order to maximize the bound on the admissible disturbances and/or on the delay.

This paper presents a multicriteria image-based controller that allows to track moving targets with square integrable velocity. The proposed approach is based on both polytopic and norm-bounded representations of uncertainties and uses an original sector condition for the description of saturations. The controller allows to stabilize the camera despite depth uncertainty, bounds on visual features errors to ensure visibility, and limits on the camera velocity and acceleration. We determine a neighborhood of the origin inside which the system trajectories remain during the tracking. Asymptotic stability of the closed-loop system is proved when the target is at rest.

This paper addresses the stabilization problem of singularly perturbed systems subject to actuator saturation. A solution in terms of linear matrix inequalities is proposed. The saturation is represented by means of a modified sector nonlinearity. The numerical problems due to the ill conditioning of the system model are avoided using a non-decoupling strategy. Some numerical results are also included for testing the proposed methods.

This paper addresses the problem of stability analysis for a flexible cantilever beam which is subject to amplitude limitations in actuator and sensor. The design of anti-windup schemes is considered in order to enlarge the region of stability of the closed-loop system. Based on the modelling of the saturated system as a linear system with dead-zone nested nonlinearities, constructive stability conditions are formulated in terms of linear matrix inequalities. Some discussions about possible extensions based on the use of observer loops are provided.

This paper addresses the problems of the design of anti-windup schemes for linear systems subject to amplitude limitations in actuator and sensor. The design of anti-windup loops, using both measured and estimated variables, is considered in order to enlarge the region of stability of the closed-loop system, whereas some performance in terms of bounded controlled output is guaranteed. Based on the modelling of the closed-loop saturated system including the observer loop as a linear system with dead-zone nested nonlinearities, constructive stability conditions are formulated in terms of linear matrix inequalities by using Finsler's Lemma.

Conditions for the existence of disturbance decoupled minimal-order observers for a class of descriptor systems are presented. Basically, these conditions are associated to the solution of a generalized Sylvester equation under a constraint that describes the disturbance decoupling of the estimated state. Thus, under some structural conditions of the considered descriptor system, a sequence of coordinate transformation allows to define a reduced-order normal system. Both eigenstructure assignment and regional pole placement techniques can be applied to solve the constrained reduced-order Sylvester equation. For regional pole placement, a LMI technique is proposed and a illustrative numerical example i reported.

This paper addresses the problem of controlling a continuous-time linear system subject to actuator saturations and to L 2 -bounded disturbances. We propose LMI conditions that allow to design a state feedback saturating control law in order to satisfy the closed-loop Input-to-State stability (ISS). By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition , which encompasses the classical sector-nonlinearity condition considered in previous works, and Finsler’s Lemma , which allows to derive stabilization conditions which are potentially adapted to be cast into multiple objective control optimization problems. Relative to a previous work which proposed BMI conditions for treating a similar problem, the given LMI conditions allow to propose a more efficient convex programming design technique.

This paper addresses the problem of the determination of regions of stability for linear systems with amplitude and successive dynamics restricted actuator through anti-windup strategies. Considering a linear dynamic output feedback designed with respect to the linear system (without saturation), an anti-windup design method is investigated to guarantee both the stability of the closed-loop system and the respect of the controlled output constraints for a region of admissible initial states as large as possible. Based on the modeling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear system with dead-zone and dynamics restricted nonlinearities, LMI stability conditions are formulated. Numerical optimization procedures are discussed.

In this paper, the problem of dealing with large magnitude disturbances at the entrance of Waste Water Treatment Plants (WWTP) is investigated. To overcome the problem of actuator saturation when controlling equalization systems, the use of constrained control methods is proposed. The performance of the proposed strategy is evaluated in simulation using a model of an equalization process.