Discrete Time-delay Systems Research Articles

Stability of Discrete-Time Delayed Systems Subject to External Interference and Generalized Overflow Nonlinearities

This article concerns the stability of delayed discrete-time systems (DTSs) through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance under external interference and generalized overflow nonlinearities. The novel criteria that analyze the exponential stability of DTSs with constant state delays are presented. Moreover, an extension to attain the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance is developed to handle the external interference of systems with time-varying delays based on Wirtinger-based inequality and reciprocal convex inequality. For such systems, the presented approach ensures zero-input overflow stability as well as robustness against interferences with a guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> level. The presented methodology can also be applied to determine the minimum attenuation level to achieve the desirable performance specifications for the sake of hardware optimization. The presented criteria are less conservative than several existing criteria. The efficacy of the presented criteria is exemplified by examples.

Formula omitted] fusion estimation for uncertain discrete time-delayed Hamiltonian systems with sensor saturations: An event-triggered approach

This paper is concerned with the event-triggered H∞ fusion estimation problem for uncertain discrete-time Hamiltonian systems with time-varying delays and sensor saturations. In order to improve the efficiency of resource utilization, a component-based event-triggered mechanism is implemented on the communication path from sensors to the estimator, where each output is sent only when a prescribed event-triggering condition is satisfied. By considering the structural characteristics of discrete-time Hamiltonian systems and utilizing the Lyapunov–Krasovskii stability, sufficient conditions are established to guarantee the augmented system (i.e., the underlying system combined with the estimation error dynamics) is locally exponentially stable. Meanwhile, the estimator gain is acquired by resorting the approach of certain matrix inequality. Finally, two examples are provided to demonstrate the effectiveness of the proposed scheme.

H_infinity Stabilization of Uncertain Discrete Time-Delayed System with Actuator Saturation by using Wirtinger Inequality

H_infinity Stabilization of Uncertain Discrete Time-Delayed System with Actuator Saturation by using Wirtinger Inequality

White noise estimation for linear discrete fractional order system

&lt;abstract&gt; &lt;p&gt;The process white noise (PWN) and observation white noise (OWN) estimation problem for linear discrete fractional order systems (LDFOS) is addressed in this study. By using the Grünwald-Letnikov (G-L) operator as a definition of the discrete fractional calculus (DFC), LDFOS is transformed into a class of linear discrete time-delay systems. However, it is different from the general time-delay system, in which the time-delay part is the cumulative sum from time 0 to the previous time. Based on the orthogonal projection theorem, a suboptimal one-step predictor of LDFOS is designed. Due to the existence of cumulative sum time-delay in system, the Riccati equation has one more cumulative sum state error variance term, which is different from the classical Kalman filter (KF). Moreover, using innovation analysis technology, the filtering and fixed-lag smoothing estimators of PWN and OWN in the form of noise orthogonal projection gain matrices are derived. Finally, two simulation examples are given to verify the effectiveness of PWN and OWN estimators.&lt;/p&gt; &lt;/abstract&gt;

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

Observer-Based PID Security Control for Discrete Time-Delay Systems Under Cyber-Attacks

This article deals with the observer-based proportional-integral-derivative (PID) security control problem for a kind of linear discrete time-delay systems subject to cyber-attacks. The cyber-attacks, which include both denial-of-service and deception attacks, are allowed to be randomly occurring as regulated by two sequences of Bernoulli distributed random variables with certain probabilities. A novel observer-based PID controller is proposed such that the closed-loop system achieves the desired security level and the quadratic cost criterion (QCC) has an upper bound. Sufficient conditions are derived under which the exponentially mean-square input-to-state stability is guaranteed and the desired security level is then achieved. Subsequently, an upper bound of the QCC is obtained and the explicit expression of the desired PID controller is also parameterized. Finally, the validity of the developed design approach is verified via an illustrative example.

Guaranteed Cost Preview and Repetitive Control for Uncertain Linear Discrete Time-Delay Systems

Guaranteed Cost Preview and Repetitive Control for Uncertain Linear Discrete Time-Delay Systems

Exponential estimate with a time-varying factor for positive discrete-time systems with time-delays

We present a new method to find an α-exponential estimate for a class of positive discrete time-delay systems. Rather than finding an α-exponential estimate with a constant factor as in most of existing results, our novel idea is to find an α-exponential estimate with a decreasing factor function. As a result, we provide a smaller α-exponential estimate for the system. The effectiveness of the obtained result is illustrated through a numerical example.

State estimation and stabilisation of nonlinear networked control systems with mixed time-delay

ABSTRACT In this paper, the problems of time-delay, packet loss and quantisation for network control with global Lipschitz nonlinearity are investigated. The packet losses between the forward and backward channels are considered, and two independent Bernoulli distributions are modelled respectively. An appropriate compensation strategy is proposed to reduce the buffeting and response time of the system. A controller based on differential proportional observer is proposed. The information of estimation errors is used to optimise state estimations. Finally, a simulation example illustrates the feasibility of the method, and the comparisons with existing discrete time-delay system and distributed time-delay system prove the superiority of the method.

New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

On Stability Analysis of Discrete-Time Systems With Constrained Time-Delays via Nonlinear Halanay-Type Inequality

This letter aims to study the problem of stability for discrete-time fully nonlinear time-delay systems with constrained time-varying delays. A delays digraph is used to model the topology of the delay signals. By exploiting the Halanay technique and suitable Lyapunov functions, some sufficient conditions for the global asymptotic stability, uniform global asymptotic stability and global exponential stability are established. A matrix inequality is derived, and it is employed to prove the global exponential stability of linear discrete-time delay systems with delay signals obeying to a delays digraph. Finally, examples are given to illustrate the results.

Time domain and frequency domain model order reduction for discrete time-delay systems

This paper explores model order reduction (MOR) methods for discrete time-delay systems in the time domain and the frequency domain. First, the discrete time-delay system is expanded under discrete Laguerre polynomials, and the discrete Laguerre coefficients of the system are obtained by a matrix equation. After that, the reduced order system is obtained by using the projection matrix based on these coefficients. Theoretical analysis shows that the resulting reduced order system can preserve a certain number of discrete Laguerre coefficients of output variables in the time domain. We also derive the error bound in the time domain. Furthermore, in order to obtain the moments of the system, we approximate the transfer function of the discrete time-delay system by Taylor expansion. The basis matrices of the higher order Krylov subspace are deduced by a iterative process. Further, we prove that the reduced order system can match a desired number of moments of the original system. The error estimation is obtained in the frequency domain. Finally, two illustrative examples are given to verify the effectiveness of the proposed methods.

Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems. In this method, monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones. The Lyapunov-Krasovskii functional is allowed to increase in some steps, but the overall trend should be decreasing. The model of practical systems used for stability analysis usually contain uncertainty. Therefore, firstly a non-monotonic stability condition is derived for certain discrete time-delay systems, then robust non-monotonic stability conditions are proposed for uncertain systems. Finally, a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition. The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities (LMI) or iterative LMI based nonlinear minimization. The proposed theorems are first evaluated by some numerical examples, and then by simulation and implementation on the pH neutralizing process plant.

Non-monotonic Lyapunov-Krasovskii functional approach to stability analysis and stabilization of discrete time-delay systems

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities ( LMIs ) to study the global asymptotic stability of state-delay systems. Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.

Laguerre-domain Modeling and Identification of Linear Discrete-time Delay Systems

A closed-form Laguerre-domain representation of discrete linear time-invariant systems with constant input time delay is derived. It is shown to be useful in a l2 → l2 system identification setup (with l2 denoting square-summables signals) often arising in biomedical applications, where the experimental protocol does not allow for persistent excitation of the system dynamics. The utility of the proposed system representation is demonstrated on a problem of drug kinetics estimation from clinical data.

Interval estimation for linear discrete-time delay systems

This paper deals with the problem of interval estimation for linear discrete-time systems with a constant time delay. First, an interval observer is designed based on cooperativity and Lyapunov-Krasovskii stability analysis. Second, a zonotope-based interval estimation, which is independent of cooperativity constraint, is proposed. It integrates robust observer design, based on multiple feedbacks, with reachability analysis via zonotopes. In order to enhance the accuracy of interval estimation, an H∞ technique is introduced into observer design to reduce the effects of disturbances and noises. Finally, simulation results are given to illustrate the efficiency of the proposed method.

State-space analysis of fractional-order respiratory system models

Fractional Order Models (FOM) of the respiratory system have been used in the model-based analysis of the respiratory system. Although there are studies exploring the physiological correctness and fitting accuracy of the models, they are not analyzed in terms of interactions between parameters, time-varying dynamics and measurable signals. In this study we purpose to use state-space analysis to yield the time-varying nature of the system incorporated by the parameters, states and output. We tested the models for controllability, observability and stability characteristics while using the parameters found in the literature. Sufficient asymptotic stability bounds were driven by using stability theory of the discrete time-delay system. Results revealed that FOMs with estimated parameters offer systems with different characteristics. Thus, careful consideration must be given when interpreting estimated parameters in FOMs during respiratory tests.

Moving Horizon Estimation for Networked Time-Delay Systems Under Round-Robin Protocol

This paper is concerned with the moving horizon estimation problem for a class of discrete time-delay systems under the Round-Robin (RR) protocol. The communication between the sensor nodes and the remote state estimator is implemented via a shared network, where only one sensor node is permitted to transmit data at each time instant for the purpose of preventing data collisions. The RR protocol is utilized to orchestrate the transmission order of sensor nodes, under which the selected node obtaining access to the network could be modeled by a periodic function. A lifting technology is introduced to reformulate the system model into a linear system without delays. The aim of the addressed problem is to develop a moving horizon estimator such that the estimation error is ultimately bounded. A sufficient condition is established to ensure the ultimate boundedness in terms of a matrix inequality. Within the established theoretical framework, two optimization problems are proposed to calculate the corresponding estimator parameters according to two different performance requirements (e.g., the smallest ultimate bound and the fastest decay rate). Finally, simulation examples are given to illustrate the effectiveness of the estimator design scheme.

H∞ Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming

In this article, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control problem for a class of discrete time-delay systems is studied using databased adaptive dynamic programming (ADP) algorithm. First, the controlled system and the reference system are combined to form an augmented discrete time-delay system. Second, we transform it into a discrete time-delay system represented by system measured data, which allows the system state to be completely replaced by the data generated during system operation. Third, a novel data-based Bellman equation is derived according to the Bellman optimality principle. Then, an ADP-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control method is designed by means of the measured data. The simulation example demonstrates the effectiveness of the data-based ADP control method proposed in this article.