Stability and control synthesis for discrete-time linear systems subject to actuator saturation by output feedback

This paper presents sufficient conditions of asymptotic stability for discrete-time linear systems subject to actuator saturations with an output feedback law. The derived stability results are given in terms of LMIs. A new proof is presented to obtain previous conditions of asymptotic stability. A numerical example is used to illustrate this technique by using a linear optimization problem subject to LMI constraints

Robust H∞ Control of Takagi–Sugeno Systems with Actuator Saturation

Producción CientíficaThe robust static output feedback control for continuous-time Takagi–Sugeno systems subject to actuator saturation is solved here, including H∞ performance guarantees. Based on a polytopic model of the saturation, sufficient conditions are proposed for designing these controllers in terms of Linear Matrix Inequalities. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved easily without requiring iterative algorithms or equality constraints, moreover, the output matrix of the considered system does not require to be full row rank. Finally, some examples are presented to show the validity of the proposed methodology

A new design of robust H∞ filters for uncertain continuous-time stochastic systems

This paper is concerned with the problemof robust H∞ filtering for linear continuoustimestochastic systems with polytopic parameteruncertainties. We utilize the polynomial parameterdependent approach to solve the robust H∞ filteringproblem, and the proposed approach include resultsin the quadratic framework that entail fixed matricesfor the entire uncertain domain and results in the linearlyparameter-dependent framework that use linearconvex combinations of matrices as special cases. Newlinear matrix inequality (LMI) conditions obtainedfor the existence of admissible for the existence ofadmissible filters are developed based on homogenouspolynomial parameter-dependent matrices of arbitrarydegree. Numerical examples are provided toillustrate the effectiveness and advantages of the filterdesign methods proposed in this paper

On Stability And Performance Analysis Of Discrete-time Uncertain Systems Via Polynomially Parameter-Dependent Lyapunov Functions

This paper presents a new linear matrix inequality based stability result for uncertain discretetime linear system. which using Homogeneous Polynomially Parameter-Dependent Lyapunov Functions and a larger number of slack variables. This technique has two advantages: (1) possible to yield less conservative results, which is shown via a numerical examples; and (2) flexible to cope with more complicated problems, which is illustrated by presenting a new H∞ performance condition. It is anticipated that the idea behind this paper can be further extended to deal with synthesis problems

A two dimensional fluid model for TCP/AQM analysis

This work proposes a new mathematical model for the TCP/AQM system that aims to improve the accuracy of existing fluid models, especially with respect to the sequential events that occur in the network. The analysis is based on the consideration of two time bases, one at the queue's router level and the other at the congestion window level, which leads to the derivation of a new nonlinear two-dimensional fluid model for Internet congestion control. To avoid the difficult task of assessing stability of a 2D nonlinear dynamic model, we perform a local stability analysis of a 2D linear TCP AQM model. By constructing a new two dimensional second order Bessel Legendre Lyapunov functional, new matrix inequalities are derived to evaluate the stability of the 0-input system and to synthesize a feedback controller. Finally, two Internet traffic scenarios, with state space matrices for replicability, are presented, demonstrating the validity of the theoretical results.Comment: Active queue management, network assisted congestion control, TCP/AQM, 2D time delay systems, Roesser model, 2D second order bessel Legendre, Lyapuno

Mixed H2/H1 Filtering for Ploytopic Discrete-time Systems with Homogeneous Polynomials

This paper investigates the robust mixed H2/H1 filtering problem for linear time-invariant (LTI) discrete systems with polytopic uncertainty. The structured polynomially parameter-dependent method is used, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed methods

POLYNOMIAL STATIC OUTPUT FEEDBACK H ∞ CONTROL FOR CONTINUOUS-TIME LINEAR SYSTEMS VIA DESCRIPTOR APPROACH

International audienceThis paper deals with the problem of the robust static output feedback H ∞ control (SOFC) for continuous linear systems with polytopic uncertainties. The controller has been gotten by the use of descriptor redundancy. Under this approach a sufficient condition is provided for the existence of a solution to the problem. Thus, the advantage of this method is to obtain more free matrices in the design condition, also the polynomial approach helps to have a less conservative result. In the end, the performance of the method is shown by several examples

Robust H∞ Filters for Uncertain Systems with Finite Frequency Specifications

International audienceThis paper deals with H∞ filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman–Yakubovich–Popov lemma, polynomially parameter-dependentLyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition isobtained for analyzing the H∞performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed H∞ filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method

LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results