generalized multiple delay-dependent H∞, functional observer design for nonlinear system

Producción CientíficaFunctional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach

Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

Producción CientíficaThe robust H∞ observer-based control design is addressed here for non-linear Takagi-Sugeno (T-S) fuzzy systems with time-varying delays, subject to uncertainties and external disturbances. This is motivated by the quadruple-tank with time delay control problem. The observer design methodology is based on constructing an appropriate Lyapunov–Krasovskii functional (LKF) for an augmented system formed from the original and the delayed states. The bilinear terms are transferred to the linear matrix inequalities, thanks to a change of variables which can be solved in one step. Furthermore, by employing the L2 performance index, the adverse effects of persistent bounded disturbances is largely avoided. The proposed method has the advantage of relating the controller and Lyapunov function to both the original and delayed states. Then, the controller and observer gains are obtained simultaneously by solving these inequalities with off-the-shelf software (Yalmip/MATLAB toolbox). Finally, an application to a simulated quadruple-tank system with time delay is carried out to demonstrate the benefits of the proposed technique, showing a compromise between controller simplicity and robustness that outperforms previous approaches.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Generalized Multiple Delay-dependent H∞, Functional Observer Design for Nonlinear System

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H infini dynamic observer design for discrete-time linear systems with time varying delays based on generalized reciprocally convex matrix inequality

International audienceIn this work, we have studied the problem of designing dynamic observers (HDO) for discrete-time linear systems (DTLS) with time-varying delay (TVD) and disturbance. By designing an augmented Lyapunov-Krasovskii functional (LKF) with double summation terms using the Generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen-based inequality (JBI) and the Wirtinger-based inequality (WBI) that derive new less conservative time-dependent conditions. The resulting algebraic conditions form a set of linear matrix inequalities (LMIs) which can be solved by the LMI or YALMIP toolboxes. Furthermore, the observer under consideration has more degrees of freedom to be estimated, and is known as a generalized observer, where the proportional and proportional-integral observers are particular cases. Finally, two examples are given to demonstrate the validity and effectiveness of the findings

Design of a Functional Observer for Fuzzy Delayed Systems with Unknown Input

9th IEEE Open Conference of Electrical, Electronic and Information Sciences (eStream), Vilnius Gediminas Tech Univ, Vilnius, LITHUANIA, APR 21, 2022International audienceThis study focuses on the design of observers with unknown inputs for delayed systems represented by Takagi-Sugeno (T-S) in continuous time. When the unknown inputs are included in the state and output equations, and the delays are assumed to be bounded, fuzzy functional observers are derived. The design and analysis of the observer is based on Lyapunov-Krasovskii stability theory, and the convergence conditions of the observer are expressed in terms of linear matrix inequalities (LMIs), which can be solved numerically and symbolically using the LMI or YALMIP toolboxes. In the last part of the paper, a detailed example is proposed to prove the applicability of this technique

Mediterranean Control Conference

Producción CientíficaThis paper considers the problem of designing an H∞ observer-based controllers for continuous nonlinear systems presented by Takagi–Sugeno (T–S) model with the presence of parameter uncertainties and external disturbance. Some change of variables has been developed to linearize the bilinear terms. As a consequence, the bilinear problem conditions are converted into a set of Linear Matrix Inequalities (LMIs). Sufficient conditions f or design t he observer and controller gains are deduced in terms of LMIs conditions which can be practically solved in single step. The four-tank process application is used to show the effectiveness of the proposed method, revealing a better compromise between the simplicity and the conservatism of design method, outperforming in respect to previous approaches.Funded by Junta de Castilla y León EU-FEDER (CLU-2017-09, VA232P18, UIC225

Functional Observers Design for Linear Systems with Non-commensurate Time Varying Delays

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