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A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities.

International audience; This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov-Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach.

This paper deals with the observer design of nonlinear tubular chemical reactor models. The analysis is performed on a linearized version of the model around a steady-state profile, in which some coefficients are a function of the spatial variable. The study starts from a general model of chemical tubular reactors that will serve as a benchmark model for the formulation in the infinite dimensional Hilbert state space. The optimal output injection operator associated to the proposed observer is computed via the solution of the infinite-dimensional Riccati equation in the space variable. The performance of the observer is illustrated through numerical experiments of an industrial pulp bleaching tubular reactor model.

This article addresses the design of a nonlinear observer for nonlinear uncertain discrete-time descriptor systems. The nonlinearities that appear in both state and output equations fulfill a Lipschitz-like condition locally. Besides, the parametric uncertainties can affect the state dynamics as well as the input and output channels. The design methodology ensures input-to-state stability of the observer while minimizing an upper bound on a peak-to-peak performance index relating the disturbances/parametric uncertainties and the error in estimating a given performance signal. The observer design is cast as a convex optimization problem involving a set of linear matrix inequalities subject to a linear matrix equality constraint. The effectiveness of the proposed method is illustrated by numerical examples., SCOPUS: ar.j, info:eu-repo/semantics/published

This manuscript presents an algorithm for individual Lithium-ion (Li-ion) battery cell state of charge (SOC) estimation when multiple cells are connected in parallel, using only terminal voltage and total current measurements. For battery packs consisting of thousands of cells, it is desirable to estimate individual SOCs by only monitoring the total current in order to reduce sensing cost. Mathematically, series connected cells yield dynamics given by ordinary differential equations under classical full voltage sensing. In contrast, parallel connected cells are evidently more challenging because the dynamics are governed by a nonlinear descriptor system, including differential equations and algebraic equations arising from voltage and current balance across cells. An observer with linear output error injection is formulated, where the individual cell SOCs and local currents are locally observable from the total current and voltage measurements. The asymptotic convergence of differential and algebraic states is established by considering local Lipschitz continuity property of system nonlinearities. Simulation results on LiNiMnCoO$_2$/Graphite (NMC) cells illustrate convergence for SOCs, local currents, and terminal voltage., Comment: 7 pages, 4 figures, 1 table, accepted by 2020 American Control Conference

The dynamic output feedback stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) N-fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a dynamic output feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Furthermore, the proposed approach enables to handle with nonlinearities that are not function of the measured outputs but are sector bounded. A numerical example is considered to illustrate the effectiveness of the developed technique.

This paper provides a semidefinite optimization solution to the analysis and control of a rigid rotating spacecraft. Due to the quaternion representation of a rotating body, the nonlinearities that describe the system are polynomial in nature and may be expressed in the Differential Algebraic Representation (DAR). Once the system is in this form, it is possible to apply linear-based tools for the analysis and control design of the closed loop dynamics. The task is then reduced to that of a semidefinite optimization problem subject to constraints in the form of Linear Matrix Inequalities (LMIs).

The stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a state feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.

This paper establishes identifiability and informativity conditions for a class of deterministic linearly parametrized scalar rational models. The class considered is rational in the state and polynomial in the input. The standard definitions of identifiability and informativity for linear systems are expanded to account for the situation, common for nonlinear deterministic systems, where the identification is achieved either through the application of an informative input or via the response to an informative initial condition. We provide necessary and sufficient conditions for identifiability from the initial state, respectively from the input, as well as necessary and sufficient conditions on the initial state to produce an informative experiment. We also provide sufficient conditions on the input to be informative when the initial condition is unknown and could therefore potentially destroy the transfer of information from the input to the regressor.

International audience; This paper addresses the boundary control problem of fluid transport in a Poiseuille flow taking the actuator dynamics into account. More precisely , sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to non-linear quadratic dynamic boundary conditions by means of Lyapunov based techniques. Then, convex optimization problems in terms of linear matrix inequality constraints are derived to either estimate the closed-loop stability region or synthesize a robust control law ensuring the local closed-loop stability while estimating an admissible set of initial states. The proposed results are then applied to application-oriented examples to illustrate local stability and stabilization tools.

The advanced control of microalgal cultures usually requires the knowledge of several component concentrations, which are however not always measurable on-line. In this context, state estimation plays an important role, and software sensors should be robust to model uncertainties and measurement noise. In this study, two software sensors are designed in the form of extended Luenberger observers, using Lyapunov arguments and linear matrix inequalities (LMI). These observers are based on Droop model and a few available on-line sensors. The first observer design estimates the intracellular quota and substrate concentrations considering a linear differential inclusion modeling technique and a constant observer gain. On the other hand, the second one estimates only the intracellular quota concentration assuming uncertainties in the model parameters and a quasi-Linear Parameter Varying (quasi-LPV) representation of the nonlinear system. The results are presented considering simulated and experimental data from Dunaliella tertiolecta culture.

This paper addresses the local stabilization problem of nonlinear discrete-time systems subject to energy-bounded disturbances by means of T–S fuzzy models. A fuzzy state feedback controller is designed such that the input-to-state stability in the $$\ell _2$$ sense of the original nonlinear system is guaranteed in a bounded region of the state space. Such a region is related to the exactness of the T–S model and describes the domain around the origin where the convexity property remains valid. In addition, an estimate of the closed-loop reachable set is provided for a given class of $$\ell _2$$ disturbances. Three (convex) optimization problems are proposed to either minimize the estimate of the reachable set, improve the disturbance tolerance or minimize the $$\ell _2$$ -gain from the disturbance input to the regulated output. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.

This paper deals with the synthesis problem of multiple resonant controllers for uninterruptible-power-supply systems in a robust control framework. The controller parameters aiming the tracking of sinusoidal reference signals (with zero steady-state error) and the rejection of harmonic components of the output voltage (when supplying energy to time-varying nonlinear loads) are determined by means of a convex optimization problem subject to a set of linear-matrix-inequality constraints. Results from a 5.0-kVA experimental setup are considered to illustrate and validate the proposed approach.

This paper proposes a robust nonlinear observer for bioreactors combining the classical asymptotic observer and a nonlinear Luenberger-like observer. The resulting hybrid observer considers a new definition of the hybridization parameter which reflects the kinetic model confidence. The nonlinear observer is tuned on the basis of robust H-infinity approach and the differential-algebraic representation (DAR) of nonlinear systems. A simulated case study concerning fed-batch animal cell cultures is presented to demonstrate the potentials and advantages of the proposed approach for state estimation of bioreactors.

This paper addresses the synthesis of delay-dependent local stabilizing controllers for, possibly open-loop unstable, nonlinear quadratic systems with a varying time-delay in the state. We develop methods for designing static nonlinear quadratic state feedback controllers that guarantee the local asymptotic stability of the closed-loop system zero equilibrium point in some polytopic region of the state-space while ensuring a region of stability inside this polytope. Control designs based on either the Razumikhin or the Lyapunov-Krasovskii approaches are considered. The proposed designs are delay-dependent and are formulated in terms of linear matrix inequalities. A numerical example is presented to illustrate the application of the stabilization methods.

This paper investigates the problem of local stabilization of Markov jump nonlinear quadratic systems. A method is presented for the synthesis of a static nonlinear quadratic state feedback control law that ensures the local exponential mean square stability of the zero equilibrium point of the closed-loop system in some polytopic region of the state-space with a guaranteed region of stability inside this polytope. The proposed control design is tailored in terms of linear matrix inequalities together with convex optimization to achieve an enlarged stability region. A numerical example is presented to illustrate the application of the stabilization method.

This paper addresses the stability characterisation problem for a class of nonlinear discrete-time control systems subject to actuator saturation and energy bounded disturbance inputs. The considered class of systems covers all nonlinear discrete-time systems that can be modelled by rational difference equations. Based on quadratic and piecewise quadratic Lyapunov functions, conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability (internal stability) and the l2 input-to-state stability (external stability) of the closed-loop system. The proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible l2 disturbances, and also to obtain an estimate of the system l2-gain for an admissible set of disturbances.

This paper addresses the design of static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. Considering that a (possibly nonlinear) dynamic output feedback control law has been previously designed disregarding the saturation, a method to compute a static anti-windup gain which ensures the local stability of the closed-loop system is proposed. The results are based on a differential algebraic representation of rational systems and on a modified version of the generalized sector condition to deal with the saturation effects. From these elements, an algorithm based on the solution of LMIs is proposed to calculate an anti-windup gain to enlarge the region of attraction of the closed-loop system. Moreover, extensions of the results are presented to deal with parameter uncertainty and the presence of energy bounded disturbances. A numerical example is presented to illustrate the proposed method.

This study proposes a multiple-input/multiple-output robust approach to the control of bioprocesses based on a cascaded-loop strategy. The internal loop is a classical input-to-output feedback linearising controller which is obtained from the nominal dynamics of the bioprocess. Then, the outer loop is designed based on the internal model principle to obtain zero steady-state tracking error (and disturbance rejection) for constant signals while ensuring the robust stability of the overall closed-loop system. In addition, a robust Luenberger-like observer is proposed to estimate unmeasured state variables for the feedback linearising control law. The approach is applied to the simultaneous control of biomass and substrate concentrations in a perfusion/chemostat bioreactor, where the simulation results demonstrate the effectiveness of the proposed control strategy.

In this study, a multivariable control structure is developed to simultaneously control the concentrations of cells and of one of the nutrients in an animal cell cultivation system operated in perfusion. A cascade control structure is considered consisting of (i) an inner loop with a partially linearizing feedback controller, tuned so as to ensure robustness with respect to parameter uncertainties and non-canceled nonlinearities; and (ii) an outer loop involving two linear predictive controllers. The resulting control strategy shows robustness and performance properties similar to more computationally demanding strategies (such as a multivariable nonlinear MPC strategy), while requiring less measurements and involving an easier implementation.

This paper addresses the local stabilization problem of SISO nonlinear quadratic discrete-time systems subject to logarithmic quantization. The sector bound approach is applied to derive LMI-based conditions for synthesizing a stabilizing linear controller (both state and dynamic output feedback) while either maximizing the set of initial states assuming a given quantizer or minimizing the quantization density for a given set of initial states. A numerical example is presented to illustrate the application of the derived results.

This paper addresses the problem of local stabilization of open-loop unstable nonlinear quadratic state-delayed systems with a guaranteed region of stability. For some polytopic region of the state-space containing the origin, we develop linear matrix inequality based methods for designing nonlinear static state feedback controllers by considering either the Lyapunov-Razumikhin approach or a Lyapunov-Krasovskii functional. A numerical example illustrates the potentials of the proposed local stabilization methods.

SUMMARY This paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete-time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete-time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Uma metodologia para o projeto de controladores robustos foi desenvolvida para bioreatores operando em modo descontínuo com alimentação. Inicialmente, apresenta-se um modelo geral que descreve a dinâmica do crescimento da bactéria Escherichia Coli e da levedura Saccharomyces Cerevisiae que são atualmente os dois microorganismos mais utilizados na indústria biotecnológica. A partir do modelo dinâmico da cultura de microorganismos, busca-se projetar uma lei de controle que mantenha a concentração do produto secundário em níveis próximos a zero visando, desta forma, maximizar a produção de biomassa. Com este objetivo, a dinâmica não linear é descrita em termos de parâmetros variantes no tempo (abordagem quasi-LPV) possibilitando a utilização da formulação por desigualdades matriciais lineares para o projeto da dinâmica livre resultante da aplicação de uma lei de controle do tipo linearizante parcial. As condições propostas permitem garantir a estabilidade robusta do sistema em malha fechada frente a incertezas paramétricas, além de assegurar um certo desempenho com relação a perturbações. Para verificar o comportamento da metodologia proposta, vários testes por simulação são realizados para avaliar o comportamento da estratégia proposta em relação a trabalhos disponíveis na literatura especializada A methodology for the robust control design of a class of bioreactors operating in fed-batch mode is proposed. Firstly, a general model is presented to describe the growing dynamics of the bacteria Escherichia Coli and the yeast Saccharomyces Cerevisiae cultures, which are the most employed microorganisms applied in biotechnological industry. From this model, the paper proposes a control law that regulates the by-product concentration in small levels (i.e., close to zero) aiming to maximize the biomass concentration. To this end, the nonlinear dynamics of the bioreactor is rewritten in terms of time-varying parameters (quasi-LPV approach) in order to apply the linear matrix inequality framework for designing the free dynamics resulting from a partial feedback linearizing strategy. The proposed design conditions provide the robust stability of the closed-loop system while ensuring some performance w.r.t. disturbance signals. To verify the behavior of the closed-loop system, several simulation based tests are carried out to evaluate the controller performance against some recent strategies proposed in the specialized literature

This work addresses the design of state feedback controllers for locally stabilizing open-loop unstable quadratic systems with guaranteed stability domain and performance. First, a method is derived to design a stabilizing nonlinear static state feedback controller, which is quadratic in the system state, while providing an enlarged stability region for the closed-loop system. The stabilization method is then extended in three directions. The first one is to ensure a quadratic regulator-type performance, the second is the local stabilization, in sense of integral input-to-state stability, of quadratic systems disturbed by energy-bounded exogenous signals, whereas the third extension provides a solution to the H∞ control problem. The developed control methods are tailored via finite sets of state-dependent linear matrix inequalities. Several numerical examples are presented to illustrate the potentials of the proposed controller designs.

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 work presents a (numerical) technique to the local stability analysis of feedback linearizing control schemes for a class of uncertain nonlinear systems. A nonlinear decomposition of vector functions is applied to transform the Lyapunov stability conditions into a set of state-and parameter-dependent LMI (linear matrix inequality) constraints, which are numerically solved in a finite set of points. The proposed method can deal with a large class of nonlinear systems as well as very complex Lyapunov function candidates. In addition, a maximized level set of the Lyapunov function is proposed as an estimate of the system stability region.

This paper proposes a linear matrix inequality based method to the estimation of a robust domain of attraction for a class of discrete-time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete-time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. A numerical example illustrates the application of the proposed method.

This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach.

This paper addresses the design of robust $H_{\infty}$ filters for a class of nonlinear systems subject to uncertain, possibly time-varying, parameters. The nonlinear system is described by a differential-algebraic representation, which can model the whole class of systems with rational functions of the state and uncertain parameters, as well as some trigonometric nonlinearities. The admissible values of the uncertain parameters and their rate of variation are assumed to belong to a given polytope. A linear matrix inequality methodology is proposed for designing full-order robust linear filters with a minimized upper-bound on the $\mathcal{L}_2$-gain of the noise-to-estimation error operator for all admissible uncertainty. In order to improve the performance of the latter filter, the methodology is then extended to the design of high-order linear filters. Numerical examples are presented to demonstrate the effectiveness of the proposed filter designs.

Abstract This work proposes a robust control strategy for the optimizing control of fed-batch cultures of S. cerevisae. The process dynamics is characterized by a nonlinear kinetic model based on the bottleneck assumption and ethanol inhibition for a possible excess of substrate feeding. The control strategy is based on the feedback linearization technique, where the resulting free linear dynamics is designed so as to ensure a certain robustness to plant parameter variations. A feedforward loop achieves the correct critical substrate value, which is a function of the ethanol and oxygen in the culture medium. In addition, a robust Luenberger-like observer is designed taking plant parameter variations into account. Numerical experiments demonstrate the potential of the proposed approach as a tool for control design of fed-batch cultures.

A convex approach to robust regional stability analysis of a class of nonlinear state-delayed systems subject to convex-bounded parameter uncertainty is proposed. Delay-dependent conditions are developed to ensure system robust local stability and obtain an estimate of a domain of attraction of the origin inside a given polytopic region of the state-space. This approach is then extended to provide a delay-dependent solution to the problem of @?"2-gain analysis. The proposed approach is based on a Lyapunov-Krasovskii functional with polynomial dependence on the system state and uncertain parameters and is formulated in terms of linear matrix inequalities. Numerical examples illustrate the potentials of the derived results.

This paper proposes a convex approach to regional stability analysis of a class of nonlinear state-delayed systems subject to convex-bounded parameter uncertainty. Delay-dependent conditions are developed to ensure the system robust local stability and obtain an estimate of a domain of attraction of the origin inside a given polytopic region of the state-space. The proposed approach is based on a Lyapunov-Krasovskii functional with polynomial dependence on the system state and uncertain parameters and is formulated in terms of linear matrix inequalities. Numerical examples illustrate the potentials of the derived results.

This paper proposes a convex approach to regional stability and ℒ2-gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input-to-output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential-algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ2-gain of the input-to-output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full-order) output feedback controller with a guaranteed bound on the ℒ2-gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.

This paper proposes a convex approach to the design of robust bilinear H ∞ filters for a class of nonlinear discrete-time systems subject to convex-bounded uncertain constant parameters. The nonlinear system is described by a difference-algebraic representation, which can model the whole class of system with rational functions of the system state and uncertain parameters, as well as some trigonometric nonlinearities. The filter design is based on Lyapunov functions with rational dependence on the system state and uncertain parameters and it is given in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed method.

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result

This paper addresses the design of robust H 2 filters for a class of nonlinear systems subject to uncertain parameters belonging to a given polytope. The nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. Linear matrix inequality conditions based on a parameter-dependent Lyapunov function are proposed to design a robust linear filter which ensures an optimized upper-bound on the worst-case asymptotic estimation error variance.

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.

A new methodology based on the linear matrix inequality (LMI) framework is presented for the computation of polynomial Lyapunov functions for differential–algebraic nonlinear systems. The method is applied for estimating the domain of attraction of equilibria and also as a control design tool to increase the damping of the system. Numerical examples are used to demonstrate the approach. The results show the potential of the proposed approach as a tool for analysis and control design. Copyright © 2004 John Wiley & Sons, Ltd.

This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with time-invariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach. Este artigo trata do problema de determinar regiões de estabilidade robustas para uma classe de sistemas não lineares com incertezas invariantes no tempo e sujeitos à saturação no sinal de controle. O sistema não linear é representado por uma equação algébrico- diferencial onde as matrizes do sistema são funções racionais dos estados e incertezas e a saturação no controle é representada como uma condição de setor. As condições de estabilidade local propostas são expressas por LMIs e estão baseadas numa função de Lyapunov que é polinomial (ordem 4) nos estados e quadrática nos parâmetros incertos. Para estimar a região de estabilidade robusta propõe-se um problema de maximização da maior curva de nível da função de Lyapunov dentro de um politopo dado representando as condições iniciais. Os resultados são ilustrados através de um exemplo numérico.

The problem of estimating robust stability domains for a class of nonlinear systems subject to actuator saturation is addressed. The unforced nonlinear system is represented by differential-algebraic equations which are linear with respect to the state and algebraic vectors, and the saturation nonlinearity is modelled by a sector bound condition. The system stability is analyzed by means of linear matrix inequality conditions based on non-quadratic Lyapunov functions. A non-saturated control strategy is also proposed in order to stabilize the system while maximizing the stability domain.

In this paper, we consider the problem of guaranteed cost control for a class of uncertain nonlinear systems. We derive linear matrix inequality conditions for the regional robust stability and performance problems based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. The performance index is calculated over a set of initial conditions. Also, we discuss the synthesis problem for a class of affine control systems. Numerical examples illustrate our method.

This paper addresses the input-to-state stabilization problem in the l2 sense for a class of discrete-time nonlinear systems described by Takagi-Sugeno (T-S) fuzzy models. It turns out that T-S models accurately represent the original system in some bounded region of the state space (namely the T-S domain of validity). Thus, a numerical and tractable solution to the local stabilization problem is proposed while providing an estimate of the closed-loop stability region (a positively invariant set belonging to the T-S domain of validity which bounds the state trajectory driven by admissible disturbance inputs). This paper concentrates on the state feedback design problem in which the feedback gain is computed by means of a convex optimization problem in terms of linear matrix inequality constraints. Numerical examples illustrate the technique demonstrating the effectiveness of the approach as a control design tool for nonlinear discrete-time systems.

This paper focuses on the problem of static anti-windup design for a class of multivariable nonlinear systems subject to actuator saturation. More precisely, a convex approach is proposed to compute a static anti-windup gain which ensures regional stability for the closed-loop system assuming that a nonlinear dynamic output feedback controller is previously designed to stabilize the nonlinear system. The results are based on the differential-algebraic representation of rational systems and a modified sector bound condition is applied to model the saturation effects. From these elements, LMI based conditions are devised to compute an anti-windup gain for enlarging the closed-loop region of attraction. A numerical example is given to illustrate the proposed method.

This paper deals with the problem of local stabilization, with a guaranteed stability domain and performance, of open-loop unstable quadratic discrete-time systems. For some polyhedral region of the state-space containing the origin, a method is derived for designing a nonlinear static state feedback controller that ensures an enlarged stability domain for the closed-loop system. The stabilization method is then extended to ensure a quadratic performance for a set of admissible initial states. The controller designs are tailored via finite sets of state-dependent linear matrix inequalities. Numerical examples are presented to illustrate the proposed control designs.

This work addresses the problem of designing a state feedback control law for locally stabilizing open-loop unstable quadratic systems with a guaranteed stability domain. Firstly, for some polytopic region of the state-space containing the origin, a method is derived to design a nonlinear static state feedback controller which maximizes the size of the closed-loop system stability domain. Then, the proposed method is extended to handle systems disturbed by energy-bounded signals. The controller designs are tailored via a finite set of state-dependent linear matrix inequalities. Numerical examples are given to illustrate the potentials of the proposed control designs.

This paper addresses the stability characterization problem for a class of nonlinear discrete-time control systems subject to actuator saturation and energy bounded disturbance inputs. The considered class of systems covers all nonlinear discrete-time systems that can be modeled by rational difference equations. The results are based on a recursive algebraic representation of the nonlinear control system and a generalized sector bound condition to deal with the saturation effect. From these elements, LMI based conditions are proposed to analyze the asymptotic stability and both the L 2 input-to-state and input-to-output stability properties. The proposed conditions are then incorporated into convex optimization problems to either maximize an ellipsoidal estimate of the region of attraction or a bound on the admissible L 2 disturbances, and also to minimize a bound on the system L 2 -gain.

This chapter outlines a generic method to the analysis of eye-in-hand position-based or image-based visual servos. This analysis is said to be “multicriteria” as both the convergence and the fulfillment of important constraints can be assessed, including the target visibility, the avoidance of actuators’ saturations, and the exclusion of 3D areas. The field of nonlinear “rational” systems is first shown to constitute a sound and versatile framework to the problem. The fundamentals of a solution based on Lyapunov theory are overviewed next, together with the noteworthy difficulties raised by robotics. Constructive results are finally presented, on the basis of biquadratic or piecewise-biquadratic Lyapunov functions, leading to feasibility/ optimization programs subject to linear matrix inequalities (LMIs). A case study illustrates the approach.

This work applies the quasi-LPV technique to the design of robust observers for a class of bioreactors. The system nonlinearities are modeled in terms of two time varying parameter vectors, θ(t) and δ(t). The vector θ(t) contains all nonlinear terms that are only function of the measurements, whereas the remaining terms are lumped into the vector δ(t). Then, a θ(t) parameter-dependent Luenberger-like observer is proposed, where the design conditions are given in terms of linear matrix inequality constraints. These conditions ensure regional stability w.r.t. to a set of admissible initial conditions and also minimizes an upper-bound on the L 2-gain of the error system. These results are applied to a high cell density bioreator.