Discrete Time-delay Systems Research Articles

Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional

Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional

Robust Controller Design of Uncertain Discrete Time-Delay Systems With Input Saturation and Disturbances

This technical note deals with the problem of robust controller design of uncertain discrete time-delay systems subject to control input saturation and bounded external disturbances. A sufficient condition is obtained, which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed-loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain. An iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers. A simulation example is provided to demonstrate the effectiveness of the proposed method.

Cyclic invariance for discrete time-delay systems

This technical communique introduces a new concept of set invariance with respect to linear discrete time dynamics affected by delay. We are interested in the definition and characterization of sequences of cyclically invariant subsets in the state space. The algebraic conditions established in the late ’80s for linear dynamics are generalized to invariance analysis in the presence of delays for given sequences of polyhedral sets.

A new recursive algorithm for simultaneous identification of discrete time delay systems

A new algorithm for simultaneous online identification of unknown time delay and parameters of discrete-time delay systems is proposed in this paper. This algorithm consists in constructing a linear-parameters formulation and using the recursive least squares approach to solve the obtained system. Simulation example and experimental test results are presented to illustrate the performance of the proposed approach.

Guaranteed cost D-stabilization and H∞ D-stabilization for linear discrete time-delay systems

The problems of robust guaranteed cost D-stabilization and H∞ D-stabilization are investigated in this paper for linear discrete time-delay systems. Under the framework of direct approach, sufficient conditions of robust guaranteed cost D-stability and H∞ D-stability are proposed in terms of linear matrix inequality (LMI) respectively. Furthermore, design methods of optimal guaranteed cost D-stabilization controller and optimal H∞ D-stabilization controller are given. The controllers not only guarantee that all poles of the closed-loop system remain inside the specified disk D(α,r), but also minimize the quadratic performance index (for the case of guaranteed cost D-stabilization) or the exogenous disturbance attenuation level (for the case of H∞ D-stabilization). Numerical examples are provided to illustrate the effectiveness of the proposed methods.

Mean square robust stability of stochastic switched discrete-time systems with convex polytopic uncertainties

This article is concerned with mean square robust stability of stochastic switched discrete time-delay systems with convex polytopic uncertainties. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the mean square robust stability for the stochastic switched system with convex polytopic uncertainties is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

Robust Stability and Constrained Stabilization of Discrete-Time Delay Systems

This paper revisits the problem of robust stability and stabilization of uncertain time-delay systems. We focus on the class of non-negative discrete-time delay systems and show that it is asymptotically stable if and only if an associated non-negative system without delay is asymptotically stable*. This fact allows one to establish strong result on robust stability and stability radius for this class of systems. An alternative representation of delay systems is also constructed whereby its system matrix is in block companion from. Under the assumption of non-negativity for delay systems, this alternative form represents a conventional non-negative system and similar strong robust stability results are derived. Finally, we consider the problem of constrained stabilization and provide a new LMI feasibility solution for it. This makes it possible to stabilize a general discrete-time delay system such that the closed-loop system admits non-negative structure with desirable properties.

New sufficient conditions for the asymptotic stability of discrete time-delay systems

This paper is concerned with asymptotic stability of switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability for the system is designed via linear matrix inequalities. Numerical example is included to illustrate the effectiveness of the result.

Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay

In this paper, we study the dynamics of an SIR epidemic model with a logistic process and a distributed time delay. We first show that the attractivity of the disease-free equilibrium is completely determined by a threshold R0. If R0⩽1, then the disease-free equilibrium is globally attractive and the disease always dies out. Otherwise, if R0>1, then the disease-free equilibrium is unstable, and meanwhile there exists uniquely an endemic equilibrium. We then prove that for any time delay h>0, the delayed SIR epidemic model is permanent if and only if there exists an endemic equilibrium. In other words, R0>1 is a necessary and sufficient condition for the permanence of the epidemic model. Numerical examples are given to illustrate the theoretical results. We also make a distinction between the dynamics of the distributed time delay system and the discrete time delay system.

Impulsive Networked Control for Discrete-time Delayed Systems

This paper investigates the impulsive networked control issue for discrete-time delayed systems (DDSs). An impulsive networked control scheme is proposed for DDSs. Under the impulsive control, the DDS is changed to a discrete-time impulsive hybrid system. Two cases (with/without network-induced delay) are studied respectively for the impulsive control signals. By utilizing methods such as matrix spectrum and eigenvalue theory and dwell time, global uniform exponential stability (GUES) criteria are derived for the discrete-time impulsive hybrid system, under which exponential stabilization is achieved for the DDS. Moreover, the obtained results are used to design the impulsive consensus control for discrete-time delayed networks (DDNs) with non-identical nodes, and the exponential impulsive networked consensus is realized for DDNs. Finally, one example with numerical simulations is worked out for illustration.

Delay-Dependent Stability Analysis of Discrete Time Delay Systems with Actuator Saturation

This paper focuses on the study and the characterization of stability regions of discrete time systems with a time varying state delay subjected to actuator saturation through anti-windup strategies. Delay-dependent stability conditions are stated in the local as well as global context. An optimization procedure to maximize the estimate of domain of attraction is given. The proposed technique is illustrated by means of numerical examples.

Guaranteed Cost for Uncertain Discrete-Time Delay Systems

The paper proposes a dynamic output feedback cost guaranteeing control for uncertain discrete-time delay systems, where the unknown nonlinearities/uncertainties of the system are permitted to take their values in a fairly general set. The delays are considered to be unknown time varying functions with known bounds. The sufficient condition of the existence of the guaranteed cost is given by LMIs.

Stabilization of Unknown Nonlinear Discrete-Time Delay Systems Based on Neural Network

This paper discusses about the stabilization of unknown nonlinear discrete-time fixed state delay systems. The unknown system nonlinearity is approximated by Chebyshev neural network (CNN), and weight update law is presented for approximating the system nonlinearity. Using appropriate Lyapunov-Krasovskii functional the stability of the nonlinear system is ensured by the solution of linear matrix inequalities. Finally, a relevant example is given to illustrate the effectiveness of the proposed control scheme.

A SWITCHING RULE FOR THE ASYMPTOTIC STABILITY OF UNCERTAIN DISCRETE-TIME SYSTEMS

This paper is concerned with asymptotic stability of uncertain switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability for the uncertain system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays

This paper proposes an exponential stabilization control method for uncertain Takagi–Sugeno fuzzy systems with state and input delays via output feedback. First, a unified memoryless fuzzy observer-based control method is introduced for stabilizing continuous and discrete uncertain time-delay fuzzy systems. Then, the exponential stability conditions are derived and converted to solving linear matrix inequality (LMI) problems. Based on the developed novel LMI algorithms, the controller and observer gains are able to be separately designed even in the presence of modelling uncertainty, state delay, and input delay. In comparison with existing techniques the proposed technique produces controlled states and state estimation errors that are guaranteed to exponentially converge to zero via output feedback. This is a major breakthrough for the control of uncertain systems with both state and input unavailable time-varying delays. Finally, two studies are carried out on continuous and discrete time-delay systems. Numerical simulation and comparison results demonstrate the quality of the obtained performance.

Stability and stabilization of switched linear discrete-time systems with interval time-varying delay

This paper deals with stability and stabilization of a class of switched discrete-time delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

Robust H∞ sliding mode control for discrete time-delay systems with stochastic nonlinearities

This paper is concerned with the robust H∞ sliding mode control (SMC) problem for a general class of discrete time-delay uncertain systems with stochastic nonlinearities. The time-varying delay is unknown with given lower and upper bounds, and the stochastic nonlinearities are described by statistical means. The purpose of the problem addressed is to integrate the SMC method with the H∞ technique such that, for all admissible parameter uncertainty, unmatched stochastic nonlinearities, time-varying delay and unmatched external disturbance, the closed-loop system is asymptotically mean-square stable while achieving a prescribed disturbance attenuation level. Sufficient conditions are presented to ensure the desired performance of the system dynamics in the specified sliding surface by solving a semi-definite programming problem. Moreover, a discrete-time SMC law is synthesized to ensure the reaching condition. A simulation example is given to illustrate the validity of the proposed SMC scheme.

Persistent bounded disturbance rejection for discrete-time delay systems

In this article, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-function method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities to guarantee the desired ℓ1-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.

Reliable H ∞ control for discrete uncertain time-delay systems with randomly occurring nonlinearities: the output feedback case

This article is concerned with the reliable H ∞ output feedback control problem against actuator failures for a class of uncertain discrete time-delay systems with randomly occurred nonlinearities (RONs). The failures of actuators are quantified by a variable varying in a given interval. RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a Bernoulli distributed white sequence with a known conditional probability. The time-varying delay is unknown with the given lower and upper bounds. Attention is focused on the analysis and design of an output feedback controller such that, for all possible actuator failures, RONs, time-delays as well as admissible parameter uncertainties, the closed-loop system is exponentially mean-square stable and also achieves a prescribed H ∞ performance level. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach.

Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements

In this paper, the exponential H∞ filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements. The measurement missing phenomenon, which is related to the modes of subsystems, is described in the form of random matrix function and the missing probability of each sensor at every mode is governed by an individual random variable taking values in the interval [0,1] . This description of missing measurements is more general than the existing ones, where the missing probability is described by a Bernoulli distribution white sequence or a certain diagonal matrix. By using Lyapunov method and the properties of conditional mathematical expectation, we propose a novel approach to achieve the delay-dependent exponential stability criterion such that the filtering error system is mean-square exponentially stable and satisfies a prescribed H∞ performance level. Moreover, there is no equation restriction on decay rate. Then, based on the obtained sufficient criterion, the filter matrices can be directly characterized by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the main result.