Uncertain Time-varying Delay Systems Research Articles

Observer-based state tracking control of uncertain stochastic systems via repetitive controller

ABSTRACTThis paper develops the repetitive control scheme for state tracking control of uncertain stochastic time-varying delay systems via equivalent-input-disturbance approach. The main purpose of this work is to design a repetitive controller to guarantee the tracking performance under the effects of unknown disturbances with bounded frequency and parameter variations. Specifically, a new set of linear matrix inequality (LMI)-based conditions is derived based on the suitable Lyapunov–Krasovskii functional theory for designing a repetitive controller which guarantees stability and desired tracking performance. More precisely, an equivalent-input-disturbance estimator is incorporated into the control design to reduce the effect of the external disturbances. Simulation results are provided to demonstrate the desired control system stability and their tracking performance. A practical stream water quality preserving system is also provided to show the effectiveness and advantage of the proposed approach.

Robust fault reconstruction based on sliding mode observer for a class of uncertain time-varying delay systems: a rocket motor system application

In this paper, we present an extended sliding mode observer (SMO) design method for robust actuator fault reconstruction for a class of linear uncertain delayed systems. The uncertainty considered is matched and bounded. In meantime, the time-varying delay is unknown, bounded and affects simultaneously the input and the state of the system. Using the H1 concept and applying the equivalent output error injection idea from previous works in fault detection and isolation (FDI) scheme, the estimate actuator fault signal is designed with the proposed observer by minimising the uncertainty and the time-varying delay effects. Therefore, this problem is solved via a bounded real lemma (BRL) and the linear matrix inequalities (LMIs) optimisation. A rocket motor system is included to illustrate the efficiency of the proposed method. Even, in the presence of the uncertainty and the time-varying delay, the results of the simulation demonstrate that the proposed schemes can successfully estimate the system states and reconstruct the unknown actuator fault.

Robust fault reconstruction based on sliding mode observer for a class of uncertain time-varying delay systems: a rocket motor system application

Robust fault reconstruction based on sliding mode observer for a class of uncertain time-varying delay systems: a rocket motor system application

Further improvement in delay‐dependent finite‐time stability criteria for uncertain continuous‐time systems with time‐varying delays

The problem of finite-time stability for uncertain time-varying delay systems with non-linear perturbations and parametric uncertainties and switched time-delay systems is studied. New integral inequality with exponential function is proposed to solve the stability problem. By using a suitable form of Lyapunov–Krasovskii-like functional (LKLF) with exponential function, the integral inequality and estimations of LKLF in the initial and the current time, new delay-dependent and less conservative stability criteria have been derived in terms of linear matrix inequalities. The average dwell time approach is used to study the FTS of switched time-delay systems. Five numerical examples are given to show the effectiveness of the obtained results.

Robust Delay-Derivative-Dependent Sliding Mode Observer for Fault Reconstruction : A Diesel Engine System Application

In this paper, a new delay-derivative-dependent sliding mode observer (SMO) design for a class of linear uncertain time-varying delay systems is presented. Based on this observer, a robust actuator fault reconstruction method is developed. In the meantime, the considered uncertainty is bounded and the time-delay is varying and affects the state system. Besides, the dynamic properties of the observer are analyzed and the reachability condition is satisfied. Applying the developed SMO, the $$H_\infty $$H? concept and a delay-derivative-dependent bounded real lemma (BRL), a robust actuator fault reconstruction is obtained wherein the effect of the uncertainty is minimized. Also, both the SMO and the BRL are delay-derivative-dependent which reduces the time-varying delay conservatism on the state estimation and on the fault reconstruction. A diesel engine system is included to illustrate the validity and the applicability of the proposed approaches.

Robust exponential [formula omitted] control for uncertain time-varying delay systems with input saturation: A Markov jump model approach

This paper is concerned with the state feedback stabilization problem for uncertain time-varying delay systems with input saturation. Based on the stochastic property of time-varying delay, the considered system can be transformed into a continuous Markov jump system with stochastic delays, where the growth trend and the maximum value of the time-varying delay are limited. The problem we address is to design a robust state feedback controller which can switch with time-varying delay in terms of Markov process, such that the system is exponentially mean-square stable with disturbance attenuation γ. Conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. Finally, two examples are provided to demonstrate the effectiveness of the proposed approach.

H∞ approach to monotonically convergent ILC for uncertain time-varying delay systems

This paper deals with iterative learning control (ILC) design for uncertain time-delay systems. Monotonic convergence of the resulting ILC process is studied, and a sufficient condition within an H∞-based framework is developed. It is shown that under this framework, delay-dependent conditions can be obtained in terms of linear matrix inequalities (LMIs), together with formulas for gain matrices design. A numerical example is provided to illustrate the effectiveness of the robust H∞-based approach to ILC designed via LMIs.

Guaranteed cost sampled-data control for uncertain nonlinear time-varying delay system

The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].

A minimal-order observer-based guaranteed cost controller for uncertain time-varying delay systems

A minimal-order observer-based guaranteed cost controller for uncertain time-varying delay systems

Comments on “Robust exponential stability for uncertain time-varying delay systems with delay dependence”

Comments on “Robust exponential stability for uncertain time-varying delay systems with delay dependence”

State observer design for non-linear uncertain time-varying delay systems with unmatched uncertainties

State feedback is a quite useful method in system control design; however, some of the system states cannot be directly measured. Thus, acquiring the desired properties of state feedback control is a barrier. Fortunately, the state observer could be an elegant solution to such a problem. In this paper, based on sliding mode control (SMC) theory, a new sliding mode observer (SMO) for a class of non-linear uncertain time-varying delay systems with unmatched uncertainties is proposed. As is well known, during the sliding mode, the system behaviour has an invariance property, which is independent of matched uncertainty, but it is not invariant to the unmatched uncertainty and this usually restricts the applications of the results. Therefore, we make an attempt to extend the famous Luenberger observer to generate a new SMO scheme. With the proposed SMO, the estimation errors asymptotically tend to zero if the matching condition is satisfied, and the effects of the unmatched parts on the estimation errors can be uniformly ultimately bounded if the matching condition is not satisfied. A numerical example with a series of simulation studies is given to demonstrate the effectiveness of the proposed approach.

The design of a hybrid output feedback controller for an uncertain delay system with actuator failures based on the switching method

This paper focuses on the design problem of a hybrid dynamical output feedback controller for exponential stabilization of a class of uncertain time-varying delay systems with actuator failures. By representing the time-delay system in the descriptor form and using the average dwell time technique, a new delay-dependent stabilization criterion for the existence of hybrid output feedback controllers is derived in terms of matrix inequalities. A cone complementary linearization algorithm is developed to design the hybrid output feedback controller. Finally, the effectiveness and the applicability of the proposed method are demonstrated by using two simulation examples.

Robust exponential stability for uncertain time-varying delay systems with delay dependence

Abstract This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov–Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.

Practical stabilization of a class of uncertain time-varying nonlinear delay systems

In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.

Robust guaranteed cost H∞ control for uncertain time-varying delay system

This paper studies the problem of robust H∞ guaranteed cost control for a class of time-varying uncertain continuous systems with both state and input delays. Suppose that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. A new sufficient condition of H∞ robust stabilization which satisfies guaranteed cost index is given for the systems by constructing the generalized Lyapunov function and taking the linear matrix inequality approach. Robust H∞ guaranteed cost controllers can be realized simply by solving the corresponding linear matrix inequalities so that a guaranteed cost function for the closed-loop systems has an upper bound irrespective of all admissible parameter uncertainties. Then, by iterative approach, the optimal robust H∞ guaranteed cost controllers can be obtained through the corresponding convex optimization. A numerical example is given to show the potential of the proposed technique.

Robust and guaranteed-cost filter designs of uncertain time-varying delay systems

In this paper, we consider the problems of robust filter design and guaranteed-cost filter design for uncertain time-varying delay systems. Moreover, norm bounded parameter uncertainties and convex bounded uncertainties are investigated to find an admissible robust filter which guarantees the asymptotic stability and optimal norm bound of filtering-error dynamics. The appropriate condition for the existence of filter, the robust filter-design method, and the optimal upper bound are proposed by the linear matrix inequality approach. Furthermore, the robust guaranteed-cost filter-design problem can be solved using the proposed method and proper manipulations. In this case, we present an optimization problem to obtain the optimal upper bound of the guaranteed cost and the guaranteed-cost filter-design method.

Hyperstability approach to the synthesis of adaptive controller for uncertain time-varying delay systems with sector-bounded non-linear inputs

Hyperstability approach to the synthesis of adaptive controller for uncertain time-varying delay systems with sector-bounded non-linear inputs

Hyperstability approach to the synthesis of adaptive controller for uncertain time-varying delay systems with sector-bounded non-linear inputs

In this paper, a general approach is taken to the synthesis of model reference adaptive controllers for uncertain time-varying delay systems with sector-bounded non-linear inputs via hyperstability theory. It is ensured that the proposed control system is asymptotically hyperstable for the time-varying delay system with system parameter variations, modelling errors and external disturbances. Finally, some computer simulations are given to illustrate the performance of the proposed adaptive control scheme.