Time-varying Delay Uncertainties Research Articles

On delay-interval-dependent robust stability of LPD discrete-time system with mixed time-varying delays and nonlinear uncertainties

In this work, a delay-interval-dependent robust stability problem for linear parameter dependent (LPD) discrete-time system with discrete and distributed time-varying delays and nonlinear uncertainties is addressed. By adopting combinations of mixed model transformation, various inequality expressions, utilization of zero equations, and new parameter dependent Lyapunov–Krasovskii functional, a new delay-interval-dependent asymptotic stability criterion is derived in the form of linear matrix inequalities. Moreover, an improved delay-interval-dependent asymptotic stability criterion of discrete-time linear system with discrete time-varying delay and nonlinear uncertainties is also achieved. Some numerical examples are also illustrated to exhibit the effectiveness with less conservatism of the proposed stability criterion.

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.

Simultaneous stabilization of a collection of uncertain discrete-time systems with time-varying state-delay via discrete-time sliding mode control

This paper considers the simultaneous stabilization problem which concerns finding a single controller to simultaneously stabilize a finite collection of discrete-time nonlinear systems with time-varying state delay and norm-bounded uncertainties. For this purpose, a simultaneously stabilizing discrete-time sliding mode controller (DT-SMC) is synthesized. Based on the delay-dependent Lyapunov–Krasovskii functional method, sufficient conditions are derived which guarantee the existence of a common sliding surface in terms of a nonconvex feasibility problem. The cone complementarity linearization approach is exploited to transform the nonconvex conditions into a convex optimization problem. Finally, the robust simultaneously stabilizing DT-SMC is designed in order to draw the closed-loop trajectories of each system onto the common sliding surface in finite time and to maintain it thereafter. The effectiveness of the proposed method is investigated by simulation of a practical example.

Interval type-2 fuzzy sampled-data control of time-delay systems

The problem of interval type-2 (IT2) fuzzy sampled-data stabilization is addressed for nonlinear continuous-time systems with time-varying delay and parameter uncertainties. The input-delay approach together with free-weighting and slack matrices is utilized to enforce the stability analysis, and a sufficient condition is formulated. Based on the condition, an IT2 fuzzy sampled-data controller is developed such that the closed-loop system is asymptotically stable. Illustrative examples are used to manifest the merits of this design.

Disturbance rejection for singular Markovian jump systems with time-varying delay and nonlinear uncertainties

This paper employs an active disturbance rejection technique for a class of singular Markovian jump systems with external disturbances, time-varying delay and unknown nonlinear uncertainty. Based on the improved equivalent-input-disturbance approach, a robust modified repetitive controller is proposed to the considered system to solve the periodic output tracking problem. An appropriate Lyapunov–Krasovskii functional is selected to guarantee the mean-square asymptotic admissibility of the system under study. Moreover, an explicit expression of the proposed controller is presented which has the capability of forcing the system output to exactly track any given periodic reference signal. Finally, the obtained results are validated through simulations by considering a DC motor driving model to demonstrate the effectiveness of the proposed control design technique.

Stability analysis and stabilization of a class of discrete-time nonlinear switched systems with time-delay and affine parametric uncertainty

This paper presents stability analysis and stabilization of a nonlinear switched system with subsystems which involve time-varying delay, nonlinear terms, and affine parametric uncertainties. The main goal of this paper is to construct a state-feedback controller to stabilize the closed-loop switched system, and as a special case to derive sufficient conditions to guarantee the stability of the uncontrolled switched system. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay, uncertain parameters, and the maximal bound of the nonlinear term. Finally, numerical examples are provided to verify the theoretical results and to compare the obtained results with previous researches.

Robust stabilization of time-varying delay systems with predictor-observer based controller

Abstract This papers deals with the problem of robust stabilization of a class of discrete systems with time-varying input delay and model uncertainties, where the state is assumed not to be fully accessible. Thus, a predictor-observer based controller is proposed. Furthermore, a control synthesis algorithm based on the Cone Complementarity Linearization (CCL) approach is provided to design the controller and observer gains, with the objective of improving robust performance against uncertainties in the process model and the input delay. Finally, different illustrative simulations are introduced to show the main benefits of this strategy.

Robust leader-following output regulation of uncertain multi-agent systems with time-varying delay

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of time-varying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

Design of static and dynamic output feedback controllers for a discrete‐time switched non‐linear system with time‐varying delay and parametric uncertainty

This study focuses on the stability analysis and design of output feedback controllers for a non-linear discrete-time switched system with uncertain subsystems. The considered system involves time-varying delay, non-linear terms, and affine parametric uncertainties. The main goals of this study are first to derive sufficient conditions to guarantee the stability of the unforced switched system and then, to construct two stabilising output feedback controllers (static and dynamic) to stabilise the closed-loop system with considering arbitrary switching signals. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov-Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay and uncertain parameters. Furthermore, in the proposed method, the admissible bound of time-delay and the maximum non-linearity of subsystems could be calculated. Finally, numerical examples are provided to verify the theoretical results.

Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

This paper studies the stabilization problem of discrete-time switched systems in the presence of a time-varying delay and parametric uncertainties. The main goal is to provide a state feedback controller to guarantee the stability of the closed-loop system with an evaluated average dwell time. In this regard, an appropriate Lyapunov–Krasovskii functional is constructed and the sufficient conditions for stability of the closed-loop system are developed in terms of feasibility testing of proposed linear matrix inequalities. These conditions only depend on the upper bounds of the time delay and uncertain parameters. Additionally, a numerical example is provided to verify the theoretical results.

Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

The problem of robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach is investigated. The time-varying delay and parameter uncertainties are assumed to be of an internal-like type and a structured linear fractional form, respectively. Based on a Lyapunov–Krasovskii functional in delta domain, robust ℋ∞ filter scheme is proposed. Then, a sufficient condition is established for the existence of the desired filter in terms of linear-matrix inequalities. A numerical example is provided to illustrate the design procedure of the present method.

Finite-time Stability of Uncertain Neutral-type Neural Networks with Time-varying Delay

This paper is concerned with finite-time stability for a class of neutral neural networks with time-varying delay and norm-bounded uncertainties. Delay-dependent sufficient conditions, which guarantee that the uncertain neutral neural network is finite-time stable, are proposed in terms of linear matrix inequalities by Lyapunov-Krasovskii functional method. Finally, a numerical example is given to show the effectiveness and the benefits of the proposed result.

LMI‐based criteria for robust finite‐time stabilisation of switched systems with interval time‐varying delay

This study investigates the problem of finite-time stabilisation for a class of switched linear systems with interval time-varying delay and parametric uncertainties. First, sufficient conditions for the finite-time stability of unforced switched systems are presented based on the average dwell time method and on the appropriate multiple Lyapunov-like functions that contain information regarding the lower and upper bounds of delay. A state feedback controller is then proposed for uncertain switched systems, with interval time-varying delay, which guarantees finite-time stabilisation of closed-loop systems. These conditions are formulated using a set of linear matrix inequalities and are dependent on the size of the time delay. Moreover, the criteria obtained are less conservative than some existing results because of the assumption of the upper bound of the derivative of the Lyapunov-like functions, without the neglect of any useful terms. Finally, two examples are provided to demonstrate the effectiveness of the proposed method. The first is a numerical example, and the second is a practical example involving river pollution control.

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

In this study, the problems of stabilisation for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, the authors formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Adaptive Power and Rate Control for Wireless Communication Networks with Nonlinear Channel Fading and Time-Varying Delay

This paper investigates power and rate control for uncertain wireless communication networks with nonlinear channel fading and time-varying delay. A new mathematical model of power and rate control system is derived. To compensate for the effects of nonlinear channel fading, time-varying delay, and parameter uncertainty, a power and rate controller is designed based on adaptive control technique. The performance of the closed-loop system is analyzed by using Lyapunov-Krasovskii functional and linear matrix inequality. Simulation results verify the effectiveness of the proposed controller.

Robust simultaneous fault detection and control for a class of nonlinear stochastic switched delay systems under asynchronous switching

This paper concerns the simultaneous fault detection and control (SFDC) problem for a class of nonlinear stochastic switched systems with time-varying state delay and parameter uncertainties. The switching signal of detector/controller unit (DCU) is assumed to be with switching delay, which results in the asynchronous switching between the subsystems and DCU. By constructing a switching strategy depending on the state and switching delays, new sufficient conditions expressed by a set of linear matrix inequalities (LMIs) is derived to design DCU gains. This problem is formulated as an H∞ optimization problem and both mean square exponential stability and fault detection of augmented system are considered. A numerical example is finally exploited to verify the effectiveness and potential of the achieved scheme.

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.

Robust bilateral control for state convergence in uncertain teleoperation systems with time-varying delay: a guaranteed cost control design

This paper introduces a linear matrix inequality (LMI) approach-based guaranteed cost control for the bilateral teleoperation systems. The main contribution is to take into account the most important constraints in such systems including time-varying delay and model uncertainty to guarantee robust stability and performance. Firstly, we develop a control framework for bilateral teleoperation systems based on the state convergence. Sufficient conditions in terms of LMIs are then provided to achieve the system’s robustness and transparency indices. Finally, simulation results are given to validate the effectiveness of the proposed control strategy.

Robust adaptive control of strict-feedback nonlinear systems with unmodelled dynamics and time-varying delays

ABSTRACTThis paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero.