317 research outputs found
Jensen's and Wirtinger's inequalities for time-delay systems
No full textInternational audienceIn the huge literature dedicated to stability of time-delay systems, the most popular approach remains the use of Lyapunov-Krasovskii functionals. This framework allows to study a large class of time-delay systems including constant or time-varying delays. Since several years, the main challenge is to propose new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches usually adopt the same procedure which is based on the well-known Jensen's inequality which generally induces some conservatism difficult to overcome. This paper analyses firstly the conservatism induced by the Jensen's inequality and secondly proposes a wide class of new parametrized inequalities. All these are based on an extensive use of Wirtinger inequality which has been recently introduced in Liu and Fridman [2012] and Seuret and Gouaisbaut [2012b] for stability analysis
Jensen's and Wirtinger's inequalities for time-delay systems
No full textInternational audienceIn the huge literature dedicated to stability of time-delay systems, the most popular approach remains the use of Lyapunov-Krasovskii functionals. This framework allows to study a large class of time-delay systems including constant or time-varying delays. Since several years, the main challenge is to propose new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches usually adopt the same procedure which is based on the well-known Jensen's inequality which generally induces some conservatism difficult to overcome. This paper analyses firstly the conservatism induced by the Jensen's inequality and secondly proposes a wide class of new parametrized inequalities. All these are based on an extensive use of Wirtinger inequality which has been recently introduced in Liu and Fridman [2012] and Seuret and Gouaisbaut [2012b] for stability analysis
Stability analysis for sampled-data systems with a time-varying period
No full textInternational audienceThis paper deals with a new analysis of the stability of linear systems with sampled-data inputs. Inspired by the input-delay approach and the stability of impulsive systems, the proposed method provides novel stability conditions. The stability analysis concerns both constant and time-varying sampling periods. More precisely, this article focus on ensuring stability of systems under two successive sampling periods. This result allows considering one of the periods greater than the theoretical bound, based on an estimation of the convergence rate. The delay-dependent conditions are expressed using computable simple linear matrix inequalities. Several examples show the efficiency and the limitation of such stability criteria
Partial sprectum assignment for systems with delayed state feedback
No full textWe consider the problem of controlling linear systems with scalar input by means of feedback from the delayed state. A novel scheme for computing the gain that assigns the dominant eigenvalue of the resulting system is presented. The proposed approach is appealing for its simplicity and it can be applied to a variety of situations, such as delayed output measurements or time delay in the input, with both fixed and variable known delay functions. It is possible to assign the same dominant eigenvalue for an interval of delays, and the bound on the delay is expressed through sufficient, and in some cases necessary, conditions that are easy to check. The resulting control is therefore robust with respect to the delay.We consider the problem of controlling a linear system when the state is available with a non-negligible delay (delayed-state-feedback control). In such conditions, the resulting closed-loop system is always a time-delay-system. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system while ensuring the exponential zero-state stability with a prescribed decay rate. The proposed approach is appealing for its simplicity and can be applied in both cases of constant and time-varying delays. Sufficient stability conditions, that in some cases are also necessary, are provided. Such conditions allow to easily compute a lower bound, and in some cases the exact value, of the maximum delay that ensures the prescribed closed-loop behavior (Partial Spectrum Assignment with prescribed exponential stability). © 2013 IFAC
Lyapunov-Krasovskii Functionals Parameterized with Polynomials
No full textInternational audienceA novel method based on Lyapunov-Krasovskii functionals for the stability analysis of linear systems with constant is introduced. The Lyapunov-Krasovskii functionals are provided using polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Examples show that these computationally tractable conditions can give tighter stability results than the ones in the literature
A novel stability analysis of linear systems under asynchronous samplings
No full textInternational audienceThis article proposes a novel approach to assess stability of continuous linear systems with sampled-data inputs. The method, which is based on the discrete-time Lyapunov theorem, provides easy tractable stability conditions for the continuous-time model. Su±cient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems. An additional stability analysis is provided for the cases of multiple sampling periods and packet losses. Several examples show the effciency of the method
Stability analysis of networked control systems with asynchronous sampling and input delay
No full textInternational audienceThis article proposes a novel approach to assess the stability of linear systems with delayed and sampled-data inputs. The paper considers both asynchronous sampling and input delay based on an extension of existing results on the stability of sampled-data systems to the case where a delay is introduced in the control loop. The proposed method provides easy tractable sufficient conditions for asymptotic stability of sampled-data systems under asynchronous sampling and transmission delays. The period and delay-dependent conditions are expressed using computable linear matrix inequalities. Several examples show the efficiency of the stability criteria
Exponential stability and stabilization of sampled-data systems with time-varying period
No full textInternational audienceThis article proposes a novel approach to assess the exponential stability of linear systems with sampled-data inputs. The paper considers both uncertainties in the model parameters and in the sampling period. Inspired by the input-delay approach and the stability of impulsive systems, the proposed method provides easy tractable stability conditions. Sufficient stability and stabilization conditions are provided to deal with both cases of constant and time-varying sampling periods. The period-dependent conditions are expressed using computable linear matrix inequalities. Several examples show the efficiency and the limitation of such stability criteria
Validaciones experimentales de controladores basados en datos en un convertidor boost
No full textEl objetivo de este trabajo es comprobar de forma experimental el desempeño de un controlador
basado en datos o "data-driven controller" sobre un convertidor de potencia elevador o "boost".
Dicho controlador ha sido elaborado por mi tutora Carolina Albea y su compañero Alexandre
Seuret.
Para lograr dicho objetivo, el trabajo se dividirá en tres partes:
1. Simulación del modelo teórico.
2. Simulación del circuito en PLECS.
3. Implementación en el laboratorio.
En cada parte se realiza una primera prueba del convertidor en bucle abierto para la obtención
de datos y cálculo de parámetros del controlador; y una segunda prueba en bucle cerrado del
convertidor para comprobar si el controlador calculado funciona correctamente.The aim of this work is to verify experimentally the performance of a data-driven controller on a
boost power converter. Said controller has been prepared by my tutor Carolina Albea and her
partner Alexandre Seuret.
To achieve this objective, the work will be divided into three stages:
1. Simulation of the theoretical model.
2. Simulation of the PLECS circuit.
3. Implementation in the laboratory.
In each stage, a first open-loop test of the converter is carried out to obtain data and calculate
the controller parameters; and a second closed-loop test of the converter to check if the calculated
controller works correctly.Universidad de Sevilla. Grado en Ingeniería de Tecnologías Industriale
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