Interval estimation for second-order delay differential equations with delayed measurements and uncertainties

International audienceThe interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Adaptive observers-based synchronization of a class of lur'e systems under transmission delays

In revision, submitted to Int. J. Control Theory and ApplicationsWe propose an adaptive observers-based synchronization approach for a class of chaotic Lur'e systems with slope-restricted nonlinearities and uncertain parameters, under transmission time-delays. The delay is assumed to be bounded and time varying and the uncertain parameters are assumed to be piece-wise constant. Based on the Lyapunov-Krasovskii approach, we show that for sufficiently short time-delays, master-slave synchronization is achieved and therefore, the uncertain parameters may be recovered. Then, the proposed approach is extended to the case of long constant time-delays by proposing a synchronization scheme based on cascade observers. Theoretical results are illustrated via two numerical examples

Adaptive state estimation for a class of uncertain nonlinear systems with output time-delays

International audienceIn this paper, we propose an adaptive observer for nonlinear systems with slope restricted nonlinearities, unknown parameters and delayed outputs. The delay is assumed constant and the unknown parameter is assumed piece-wise constant. Based on the Lyapunov-krasovskii approach, we show that, for sufficiently small values of the time-delay, both state estimation and parametric convergence are ensured under a condition of persistent excitation. The result is illustrated via two numerical examples

Stability Analysis for Time-Varying Systems with Delay using Linear Lyapunov Functionals and a Positive Systems Approach

International audienceWe prove stability of time-varying systems with delays, using linear Lyapunov functionals and positive systems, and we provide robustness of the stability with respect to multiplicative uncertainty in the vector fields. We allow cases where the delay may be unknown, and where the vector fields defining the systems are not necessarily bounded. We illustrate our work using a chain of integrators and other examples

Robust stabilization and observation of positive Takagi-Sugeno systems

Esta tesis propone metodologías para diseñar controladores robustos y observadores para los sistemas positivos descritos por modelos de Takagi-Sugeno (TS), lineal, inciertos, y tal vez con retraso. Las condiciones de síntesis se expresan como LMIs (desigualdades matriciales lineales). En la primera parte, se establecen las condiciones para garantizar la estabilización asintótica y la α-estabilización de los sistemas T-S lineales positivas y, tal vez afectados por incertidumbres de intervalo, usando controladores de retroalimentación de estado descompuestos. En la segunda parte, se dan las condiciones necesarias y suficientes para la estabilización de los sistemas de T-S positivos con retraso, en dos casos: cuando las variables de premisa del sistema son medibles o no. Además, el problema de diseño de control basado en observador es considerado, por las leyes de retroalimentación del estado que se pueden elegir con o sin memoria. Para mostrar la eficacia de los métodos propuestos, se proporcionan ejemplos numéricos y prácticos, dando resultados satisfactorios.Departamento de Ingeniería de Sistemas y Proceso

Interval estimation for systems with time delays and algebraic constraints

International audienceThe problem of interval observer design is addressed for a class of descriptor linear systems with delays. Two sets of conditions are proposed. First, an interval observation for any input in the system is provided. Second, the control input is designed together with the observer gains in order to guarantee interval estimation and stabilization simultaneously. Efficiency of the proposed approach is illustrated by numerical experiment