Finite-Time Stability for Discrete-Time Systems with Time-Varying Delays and Nonlinear Perturbations Using Relaxed Summation Inequality

Producción CientíficaThis article deals with the problem of delay-dependent finite-time stability (FTS) for delayed discrete-time systems with nonlinear perturbations. First, based on a Lyapunov–Krasovskii Functional, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, a new reduced free-matrix-based inequality is established to estimate the single summation term. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore our method is more effective. Thus, less conservative design conditions are obtained in this paper in terms of linear matrix inequalities (LMIs) and solved using MATLAB’s LMI toolbox to achieve the desired performance. The purpose of this paper is to derive sufficient conditions that ensure the finite-time stability of the discrete-time system. Finally, numerical examples are examined to show the advantage and effectiveness of the proposed results.MICInn, PID2021-123654OB-C31MICInn, PID2020-112871RB-C2

control based on saturated time-delay systems theory of mach number in wind tunnels

Producción CientíficaA proposal for the regulation of the Mach number in wind tunnels using static state feedback for saturated systems with delays is presented here. As these systems can be precisely represented by a time-delay model with saturating inputs, a general solution for discrete delayed systems with saturating input is first derived. This general solution is based on modeling the saturation using a Lyapunov functional, using free weighting matrices and maximizing the set of admissible initial conditions. The application of this solution to the control of the Mach number in a wind tunnel is then presented, illustrating the design procedures.MiCInn Project DPI2014-54530-

congestion control of data network by using anti-windup approach

Producción CientíficaAn Active Queue Management (AQM) scheme is design to control congestion in data networks, which includes anti-windup to deal with control signal saturation. More precisely, a methodology is proposed to design advanced AQM systems capable of regulating queue size even in the presence of significant disturbances. Hence, we first provide sufficient conditions for stabilization for the equivalent class of systems, which are derived in terms of LMI: this makes possible to derive optimization solutions that ensure performance and stability for a large domain of initial conditions. This approach is validated with a numerical example that illustrates the methodology, and the improvements with respect to previous congestion control solutions

congestion control in tcp/ip routers based on sampled-data systems theory

Producción CientíficaA methodology for designing congestion controllers, based on active queue management (AQM), is presented here. The congestion control law is derived using sampled-data H∞ systems theory. More precisely, a sampled-data state feedback that guarantees the stability of the closed-loop system and satisfies a H∞ disturbance attenuation level is derived here, based on sufficient conditions expressed in terms of linear matrix inequalities. The effectiveness of the developed technique is validated on two examples

multiclass aQM on a tCP/IP router: a control theory approach

Producción CientíficaActive queue management (AQM) is a well-known technique to improve routing performance under congested traffic conditions. It is often deployed to regulate queue sizes, thus aiming for constant transmission delay. This work addresses AQM using an approach based on control theory ideas. Compared with previous results in the literature, the novelty is the consideration of heterogeneous traffic, ie, multiclass traffic. Thus, each traffic class may have different discarding policies, queue sizes, and bandwidth share. This feature brings the proposal nearer to real network management demands than previous approaches in the literature. The proposed technique assumes that each class already has a simple controller, designed a priori, and focuses on designing a static state-feedback controller for the multiclass system, where the design is based on using LMIs for the calculations. For this, optimization problems with LMI constraints are proposed to compute the state-feedback gains that ensure stability for a large set of admissible initial conditions. These conditions ensure not only closed-loop stability but also some level of performance. As far as we know, this is the first control theory based approach for the AQM problem on TCP/IP routers that allows a multiclass AQM while also considering time-varying delays and input saturation. This is an important step to frame AQM in a more formal, yet realistic context, enabling it to address important service level agreement (SLA) directives. The proposal is tested on a simulated system at the end of this paper, showing the feasibility and performance of the approach in the presence of multiclass traffic.Junta de Castilla y León y FEDER. Grant Numbers: CLU 2017-09, UIC 23

robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

Producción CientíficaStabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.MICINnn DPI2014-54530-

Finite time stability of linear time varying delay systems using free matrix based integral inequalities

This paper discusses the problem of finite time stability (FTS) for linear delayed systems where the time-varying delay is bounded. First, based on a Lyapunov–Krasovskii Functional (LKF) which contains terms of triple integrals, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, new approximations of the single and multiple quadratic integrals that appear in the LKF derivative are established using integral inequalities, called free-matrix-based integral inequalities. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore more effective. Finally, less conservative design conditions in terms of Linear Matrix Inequalities (LMIs) are proposed and solved by the LMI Tools of MATLAB to show the advantage and effectiveness of the proposed approach

Design of Finite Time Reduced Order H∞ Controller for Linear Discrete Time Systems

The current article gives a new approach that is efficient for the design of a low-order H∞ controller over a finite time interval. The system under consideration is a linear discrete time system affected by norm bounded disturbances. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, reducing the number of variables in Linear Matrix Inequalities (LMIs). Thus, reduced order H∞ controller parameters are given to guarantee a finite time H∞ bound (FTB-H∞) for a closed-loop system. The method of the finite time stability, that is proven in this paper by the Lyapunov theory, can be applied to a wide range of process models. Numerical examples demonstrating the effectiveness of the results developed are presented at the end of this paper

Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

Stabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature

Controller synthesis for steer-by-wire system performance in vehicle

A controller with anti-windup compensator is proposed in this paper, for coping with the saturating nature where the delays are included in certain parts of the state-space representation and the perturbation must be rejected effectively to achieved the desired performance using a steer-by-wire technology that is a technique to eliminate the mechanical linkage between the steering and the front wheels. Then, a simplified and detailed description of this technology is discussed to establish a linearized mathematical model in order to ensure the robust stability of a vehicle under the complicated condition of work and road. By incorporating the delay-decomposition technique, the generalized sector condition and the Finsler's lemma, sufficient conditions in the form of LMIs are derived to satisfy the H∞ control based on the Lyapunov–Krasovskii (L–K) functional. The simulation results are presented to show that high performance and robustness are achieved