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Abstract This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.

This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods. [ABSTRACT FROM AUTHOR]

We introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω . We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system. [ABSTRACT FROM AUTHOR]

For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform GAS (UGAS), in which the decay rate and transient overshoot of solutions are requested to be uniform on bounded sets of initial states. This paper investigates this relationship for time-invariant delay systems. We show that UGAS and GAS are equivalent for this class of systems under the assumption of robust forward completeness, i.e., under the assumption that the reachable set from any bounded set of initial states on any finite time horizon is bounded. We also show that, if the state space is a space in a particular family of Sobolev or H\"older spaces, then GAS is equivalent to UGAS and that robust forward completeness holds. Based on these equivalences, we provide a novel Lyapunov characterization of GAS (and UGAS) in the aforementioned spaces. [ABSTRACT FROM AUTHOR]

We introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω. We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system.

In this paper it is considered the stabilization and control of a class of high order linear systems that are subject to constant time delay at the input-output channel. In particular, systems with two unstable poles and any number of real or complex conjugate stable poles are studied. To improve the solutions existing in the literature, a new proposal for the solution of the considered problem is taken into account consisting in the design of an observer and a ProportionalDerivative PD controller to assure stable closedloop performance, establishing by means of a frequency analysis necessary and sufficient conditions for the proposed control strategy. The proposal novelty is the inclusion of the PD control action in the observer that allows to estimate internal signals used in the solution. This configuration offers advantages in the time delay size that can be handled and on the control performance of the closed loop system. A practical design procedure is presented to determine the value of the controller gains. Numerical simulations examples are presented to show the operation of the proposal. [ABSTRACT FROM AUTHOR]

This study addresses the problem of exponential stability for switched singular state‐delayed systems with switching induced state jumps, which has not been studied up to now. The considered state delay varies in a time‐varying interval. On the basis of equivalent dynamics decomposition, a model of state jump at switching instants is firstly established under an assumption that the time length between arbitrary two adjacent switches is larger than the upper bound of the state delay. Then, a sufficient condition on exponential stability of the system under the reranged dwell‐time switching constraint is presented. The key idea is the design of a dwell‐time‐dependent generalised Lyapunov function as well as a dwell‐time‐dependent function with respect to algebraic variables and application of the Razumikhin approach. The obtained stability condition exploits the lower bound and the upper bound of the dwell time. In addition, it is independent of the size of the state delay and allows the delay to be a fast time‐varying function. Finally, two numerical examples are given to show the efficacy of the derived result. [ABSTRACT FROM AUTHOR]

Identification of time delay is a prerequisite for the realisation of control compensation. The existing researches generally assume that the system input should be monotonic, which is unsuitable for online identification due to system saturation. To solve this problem, relaxed input conditions are developed in this Letter. Then a modified least-square algorithm with forgetting factors, which has a strong ability in tracking time-varying delays, is presented. Meanwhile, two extra terms whose design parameters are adjusted online according to the input condition are added into the covariance update law to guarantee the boundedness and robustness of the algorithm. Simulation results demonstrate the superiority of the proposed method and the reasonableness of the developed input conditions. [ABSTRACT FROM AUTHOR]

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampleddata, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field.

Transmission control protocol, in the transport layer of a network, can usually detect congestion after its occurrence. Therefore, designing a robust active queue management (RAQM) is imperative to prevent congestion along with being robust against wireless environment issues such as packet error rate and fading. Moreover, a communication network suffers from input delay as well as the state delay which is multiplied to the control input signal. The main contribution of the authors' study is to design a predictive sliding mode control (PSMC) procedure as a RAQM to guarantee the input delay system stability and to regulate the queue length to the desired value. Firstly, a predictor is designed for the original system to obtain an input delay free model. Then, a RAQM is designed based on PSMC for the system with non‐singular and singular control gain. The disturbance observer ensures that the estimation error tends to zero. Unlike the prevalent procedures designed for the networks, the proposed method can avoid the singular gain problem in the control design. Furthermore, it can stabilise the system and can prevent congestion with robustness against external disturbances. Finally, the simulation results, obtained from SIMULINK and professional network simulator 2, confirm the analytical consequences. [ABSTRACT FROM AUTHOR]

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet multipliers can be characterized as eigenvalues of the monodromy operator and by the solutions of a finite-dimensional nonlinear eigenvalue problem, where the evaluation of the characteristic matrix involves solving an initial value problem. We demonstrate that such a dual interpretation can be exploited in a two-stage approach for computing dominant Floquet multipliers, where global approximation is combined with local corrections. Correspondingly, we also propose two novel characterizations of left eigenvectors. Finally, from the nonlinear eigenvalue problem formulation, we derive computationally tractable expressions for derivatives of Floquet multipliers with respect to parameters, which are beneficial in the context of stability optimization. Several numerical examples show the efficacy and applicability of the presented results. [ABSTRACT FROM AUTHOR]

This study is concerned with observer‐based fault estimation (FE) and fault‐tolerant controller design for a class of discrete‐time Takagi–Sugeno (T–S) fuzzy systems. There exist multiple time‐varying state delays, sensor and actuator faults, local non‐linear dynamics and exogenous disturbances in the systems. In comparison with the existing results, the approach suggested in this study is more flexible and feasible. By means of the n ‐step induction FE, a novel fuzzy adaptive descriptor observer is developed to obtain the n ‐step error functions. Then, an active dynamic output feedback fault‐tolerant controller is designed to stabilise the closed‐loop fuzzy system. Furthermore, a set of delay‐dependent sufficient conditions are provided by the fuzzy Lyapunov function which utilises the form of linear matrix inequalities. The stability results from the observer and the controller in this study have less conservatism compared with the ones from the existence of observers and fault‐tolerant controllers. At last, a simulation example is presented to demonstrate the advantages and effectiveness of the approach proposed in the study. [ABSTRACT FROM AUTHOR]

In high-performance field-oriented control of permanent magnet synchronous machines (PMSMs), an accurate rotor position is indispensable for the key roles in coordinate transformations. However, due to the rotor position offset error and the time delay in digital control systems, it is still challenging to obtain exact rotor position information. In this study, the influence of rotor position error on the control performance of a PMSM drive system is analysed first. Then, two novel compensation technologies, $i_d$id regulation and $i_q = 0$iq=0 methods, are proposed to accurately compensate for the rotor position for both current and voltage coordinate transformations. The advantage of the proposed scheme is that even without any prior knowledge of the system delay, the rotor position offset and compensation time coefficients can also be precisely calculated. Parameter sensitivity analysis is carried out, and compensation criteria are also provided to improve the compensation accuracy. Experimental results on a 300 kW PMSM drive system demonstrate that compared to the results achieved with conventional methods, the compensation accuracies of the phase angles used for the current and voltage coordinate transformations are increased by $6^\circ $6° and $3.1^\circ $3.1° at 5000 r/min, respectively. Consequently, the control performance and stability margin of the system are efficiently improved. [ABSTRACT FROM AUTHOR]

This study investigates the event‐triggered practical finite‐time output feedback control for a class of switched high‐order non‐linear time‐delay systems with uncertain control coefficients. A reduced‐order observer is first constructed to estimate the unmeasurable states. By adding a power integrator technique, an event‐triggered output feedback controller is designed for the nominal system. Subsequently, the constructed observer and controller are scaled with a suitable gain by homogeneous domination approach, which, together with an appropriate Lyapunov–Krasoviskii functional, can render that the uncertain switched high‐order non‐linear system with time‐varying delay is practical finite‐time stability. Finally, two examples are provided to demonstrate the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

This study is concerned with the problems of asymptotic stability analysis and stabilisation for interval type‐2 (IT2) fuzzy systems with time‐varying delays. An augmented Lyapunov–Krasovskii functional including triple‐integral terms is constructed. By the second‐order Bessel–Legendre integral inequality and the reciprocally convex combination, a good estimation of the derivative for the Lyapunov–Krasovskii functional can be derived. Thus, sufficient asymptotic stability conditions for the delayed IT2 fuzzy system are established. The proposed method provides improvements and produces better results than the existing ones in the literature. Furthermore, in light of Finsler's lemma and the obtained asymptotic stability conditions, a state feedback controller for the delayed IT2 fuzzy system is developed. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study investigates the problem of reliable mixed H∞ /passive control for Takagi–Sugeno (T–S) fuzzy semi‐Markovian jump systems under different event‐triggered schemes. An asynchronous fuzzy fault‐tolerant controller is designed to deal with the actuator failures, which results in the closed‐loop system is stochastically stable with a prescribed mixed H∞ /passive performance level even if the actuator failures appear. In order to relieve the transmission pressure over the network, the authors utilise different event‐triggered schemes and compare their ability of network resource saving. In addition, there is a difference between the system modes and the controller modes to formulate the asynchronisation phenomena. By implementing the delay system method, in combination with the free‐weighting matrix and Lyapunov–Krasovskii functional, some conditions on the performance analysis are established to ensure the stochastic stability of the system. Then, controller gain matrices and event‐triggered matrices can be obtained simultaneously based on a group of feasible linear matrix inequalities. Finally, simulations are given to show the availability of the proposed method. [ABSTRACT FROM AUTHOR]

Based on the improved radial basis function (RBF) neural networks, the distributed three‐dimension formation control scheme in the presence of dynamic uncertainties is studied for non‐linear multi‐agent systems with time delay. A virtual leader which tracks the desired signal is followed by all agents adaptively. Linear reduced‐order observers are designed on the basis of absolute and local state errors of each agent. The local state error and absolute state error are generated between neighbouring agents and each individual agent in formation, respectively. The time delay for each agent in the formation can be offset by designing a Lyapunov function, which can simplify the controller design. To deal with non‐linear dynamic uncertainties and unavoidable disturbance, improved RBF neural networks are employed. In comparison with traditional RBF neural networks, improved RBF neural networks can provide better convergence performance. Subsequently, the formation controller is designed and the stability of the systems is validated by using a new Lyapunov function. Numerical simulation is conducted to demonstrate the effectiveness of the proposed method for non‐linear multi‐agent time‐delay systems. [ABSTRACT FROM AUTHOR]

In this study, a new observer for a class of non‐linear single input/single output systems is proposed. This observer is based on a modulating function with time/output dependent coordinates transformation which transforms the original system into a like‐type observer canonical form. In the new coordinates, the initial conditions are annihilated. This property permits to construct a fast convergent deadbeat observer activated after an time delay chosen in order to avoid the singularity of the transformation at the initial time t=t0. The finite‐time convergence of the observer is established, i.e. it is shown that the estimation error is bounded in finite time. The proposed observer is used in an output feedback controller design. Using the already established results on the output feedback stabilisation of non‐linear input‐affine systems, the separation principle is addressed here and the authors show that output feedback controller guarantees under certain conditions the stability of the closed‐loop system. Two numerical examples are given to illustrate the effectiveness of the proposed observer‐based output feedback controller. [ABSTRACT FROM AUTHOR]

This study deals with proposing a Lyapunov‐based technique for stability analysis of fractional order time‐delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov–Krasovskii functionals commonly used in stability analysis of integer order time‐delay systems. As a consequence for this achievement, it is revealed that the Lyapunov–Krasovskii‐based stability conditions in integer order time‐delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann–Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different case studies. [ABSTRACT FROM AUTHOR]

In the study, the authors are interested in investigating the stability analysis and state estimation of Markov jump static neural networks subject to time delays by the feat of Bessel–Legendre inequality. A canonical Bessel–Legendre inequality, which converts the limited interval [−h,0] required in traditional Bessel–Legendre inequality to a general interval [a,b] is employed. Accordingly, compared with the existing results, the restriction is naturally relaxed and the less conservative criterion is presented. The stability analysis is complicated after constructing an enhanced Lyapunov–Krasovskii functional suitable for the canonical Bessel–Legendre inequality. Furthermore, taking account of the information of system mode, the mode‐dependent scheme is applied to the design of a state estimator. Corresponding results to the stability of the estimation error system and the acquisition of the desired observer are presented. In the end, an example, which proves the validity of the method is given. [ABSTRACT FROM AUTHOR]

This study addresses practical stability and stabilisation of switched delay systems with bounded non‐vanishing perturbations. By introducing a new method, i.e. the convergence theory of the geometric series, several stability and stabilisation criteria are derived under the average dwell switching. An example is also given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This work introduces the internally positive representation of linear time‐varying delay differential systems, in the general case of multiple time‐varying delays. The technique, previously established for the delay‐free case and recently extended to various classes of linear delay systems, aims at building a positive representation of systems whose dynamics is, in general, not definite in sign, in order to export results that only hold for positive systems to arbitrary ones. In the special case of constant matrices, this leads to a simple and easy to check condition for the delay‐independent stability of differential systems with multiple time‐varying delays. The condition is shown to be less conservative than some well‐known conditions available in the literature. Numerical examples are proposed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the authors analyse the stability of switched positive linear time‐delay systems. By developing a novel multiple discontinuous co‐positive Lyapunov–Krasovskii functional approach, the stability conditions are established for switched positive time delay systems by a linear programming approach under mode‐dependent average dwell time switching. Moreover, under average dwell time switching, the corresponding stability conditions are also proposed. It is shown that their results can obtain smaller lower bounds on dwell time. Finally, simulation results are given to show the effectiveness of their methods. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of the functional observer‐based sliding mode control (SMC) design for parametric uncertain discrete‐time delayed stochastic systems includes mismatched parameter uncertainty in the state matrix and in the delayed state matrix. Stability analysis of sliding function is presented in the time delayed stochastic system with a linear matrix inequality approach. Moreover, it is shown that the state trajectories can be driven onto the specified sliding surface despite the presence of state delay, unmatched parameter uncertainty and stochastic noise in the system. The research is motivated by the fact that the system states are not always accessible for the state feedback. Therefore, SMC is estimated using the functional observer technique. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is proposed based on Gershgorin disc theorem. The claims made are validated through numerical simulations. [ABSTRACT FROM AUTHOR]

This study focuses on the stability property of a class of distributed delay systems with constant coefficients. More precisely, the authors will discuss deeper the stability analysis with respect to the delay parameter. The authors' approach will allow to give new insights in solving the so‐called complete stability problem. There are three technical issues need to be studied: First, the detection of the critical zero roots (CZRs); second, the analysis of the asymptotic behaviour of such CZRs; third, the asymptotic behaviour analysis of the critical imaginary roots (CIRs) with respect to the infinitely many critical delays. They extended their recently‐established frequency‐sweeping approach, with which these technical issues can be effectively solved. Based on these results, a procedure was proposed, with which the complete stability analysis of such systems was accomplished systematically. Moreover, the procedure represents a unified approach: Most of the steps required by the complete stability problem may be fulfilled through observing the frequency‐sweeping curves. Finally, some examples illustrate the effectiveness and advantages of the approach. [ABSTRACT FROM AUTHOR]

In this study, the problem of finite‐time feedback stabilisation for switched linear input‐delay systems with saturating actuators is addressed by virtue of the comparison‐function‐like method. Finite‐time state feedback stabilisation is discussed and controllers are designed to make the closed‐loop systems finite‐time stable. Moreover, for the case that the states are unmeasured, observers are constructed to estimate the unavailable states and the observer–controller compensator strategy is proposed. Based on the results proposed in this study, information of transient performance of the controlled switched systems can be obtained and bounds of system trajectory are estimated. An example is employed to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The additional threshold of a mixed event‐triggering mechanism (ETM) makes it impossible to guarantee the requirement of asymptotic stability. As a consequence, it is necessary to investigate input‐to‐state practically stable (ISpS) which is a mild stability property. In this study, the authors firstly model the closed‐loop event‐triggered control system as a delayed linear parameter‐varying (LPV) systems with a mixed ETM and parameter uncertainty. Then, a co‐design condition in a sense of ISpS of controller gain and trigger parameters for the delayed LPV systems is obtained by employing the parameter‐dependent Lyapunov–Krasovskii functionals and congruent transformation method. Moreover, based on the obtained co‐design condition in a sense of ISpS, an optimisation algorithm for the tradeoffs between resource utilisation and robustness of the closed‐loop system is further proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The leader‐following guaranteed‐performance consensus problems for second‐order multi‐agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This study investigates the problem of input‐to‐state stability (ISS) and integral input‐to‐state stability (iISS) of impulsive time‐varying delayed systems. Some Lyapunov–Krasovskii‐type criteria on ISS and iISS which are effective for destabilising impulses and stabilising impulses are derived from advanced linear dissipation inequalities under average impulsive interval constraints. The conditions which require the coefficients of the linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be constants in the existing results on ISS/iISS of impulsive delayed systems are weakened. In this study, with the aid of the notions of uniformly exponentially stable function and average impulsive interval, the results allow the coefficients of the developed linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be time‐varying functions which can take both positive and negative values, and the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and enough big upper bound simultaneously. Two examples are presented to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Self‐excited milling vibrations represent an important problem in the manufacturing industry. This study presents an out‐of‐process analysis based on the Lyapunov–Krasovskii approach which provides operational guidelines for the proper selection of the cutting parameters to guarantee a stable vibration‐free process. The proposed approach considers a time‐delay two degree of freedom model and takes advantage of some useful tools of the control theory developed for time‐delay systems such as the descriptor method and the Bessel–Legendre inequalities. [ABSTRACT FROM AUTHOR]

This study investigates the stochastic suppression and stabilisation of non‐linear hybrid delay systems with general one‐sided polynomial growth condition and decay rate. Given an unstable non‐linear hybrid delay system x˙(t)=f(x(t),x(t−τ(t)),r(t),t) with general one‐sided polynomial growth condition, the authors introduce two independent Brownian noise and perturb this system into stochastic hybrid delay system dx(t)=f(x(t),x(t−τ(t)),r(t),t)dt+h(x(t),r(t),t)dB1(t)+g(x(t),r(t),t)dB2(t). It is shown that the non‐linear diffusion term g(x(t),r(t),t) may suppress the potential explosion of hybrid delay system. Under a stronger condition, another linear diffusion term h(x(t),r(t),t) will make the perturbed stochastic hybrid delay system is almost surely stable with general decay rate. [ABSTRACT FROM AUTHOR]

The authors investigate input‐to‐state stabilisation for a general non‐linear system with input delay and disturbance. With an infinite‐dimensional backstepping transformation, the original system is transferred to a target system. A delay‐compensating and disturbances attenuating control law is designed for this kind of non‐linear systems. Stability of the target system is first proved by constructing a Lyapunov functional. Equivalence of norms for original and target system is deduced. Further, input‐to‐state stabilisation for the original system under the delay‐compensating control law is drawn. [ABSTRACT FROM AUTHOR]

Predictor control for a class of multi‐input non‐linear systems with time‐ and state‐dependent input delays is considered. First, a delay‐free control law is given for the original system in the absence of delays based on the control Lyapunov function. Second, sufficient conditions are obtained and a predictor control for the original system is presented. Stability analysis is done by a Lyapunov functional. Due to the delay dependent on time and state, a region of attraction is estimated. Further, the stabilisation formula is optimal with respect to a meaningful cost functional. The proposed design is illustrated by a mobile robot with input delay. [ABSTRACT FROM AUTHOR]

This study investigates the problem of global decentralised fault‐tolerant control for a class of non‐linear large‐scale systems with unknown time‐delayed interconnections. The authors propose a novel time‐delay replacement technique. With this technique, a delay‐assumption independent controller is then developed. In addition, the delayed input variables of the fuzzy approximator are replaced by the bounded reference signals so that the global stability is achieved for the approximation‐based fault tolerant control field. In doing so, it will eliminate the limitation which is posted in estimating unknown functions in the traditional approach. The proposed controller ensures that all the signals in the closed‐loop system are globally uniformly ultimately bounded, and the tracking errors can converge to a small neighbourhood of the original point by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This study addresses the estimation problem for discrete‐time measurement‐delay systems with multiplicative noise and Markov jump. First, the state equation is converted into two equations according to the geometric arguments and flexible transformations. Then, based on the reorganised innovation approach, the finite‐horizon linear minimum mean‐square‐error estimator is derived in terms of two Riccati difference equations and two Lyapunov difference equations. Finally, under the assumptions of mean square stability of the system and ergodicity of the associated Markov chain, a sufficient condition for the existence of the infinite‐horizon estimator is presented. We provide a numerical example to manifest the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The asynchronous finite‐time dynamic output feedback control problem is concerned for switched time‐delay systems with non‐linear disturbances. By constructing multiple Lyapunov functions and resorting to the average dwell‐time approach, an asynchronous dynamic output feedback controller is designed to ensure the finite‐time stability of the resulting closed‐loop system, where asynchronous means that there is a lag between switching of controllers and subsystems. It should be pointed out that the Lyapunov function energy is allowed to increase during the running intervals of the active subsystems. Furthermore, all the conditions are formulated in forms of a set of linear matrix inequalities which can be easily solved by using the recently developed interior point method. Finally, two examples are provided to show the potential of the main results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of robust $H_{\infty}$ control for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. By using the linear matrix inequality (LMI) approach, a sufficient condition is presented for a prescribed uncertain singular system with time-delay to have generalized quadratic stability and $H_{\infty}$ performance. Furthermore, the design methods of state feedback controllers are considered such that the resulting closed-loop system has generalized quadratic stability with $H_{\infty}$ performance. By means of matrix inequalities, sufficient conditions are derived for the existence of memory-less and memorial static state feedback controllers. The controllers are obtained by the solutions of matrix inequalities. [ABSTRACT FROM AUTHOR]

This paper describes a variable structure control for fractional-order systems with delay in both the input and state variables. The proposed method includes a fractional-order state predictor to eliminate the input delay. The resulting state-delay system is controlled through a sliding mode approach where the controller uses a sliding surface defined by fractional order integral. Then, the proposed control law ensures that the state trajectories reach the sliding surface in finite time. Based on recent results of Lyapunov stability theory for fractional-order systems, the stability of the closed loop is studied. Finally, an illustrative example is given to show the interest of the proposed approach. [ABSTRACT FROM AUTHOR]

Projection-based force-reflection (PBFR) algorithms have been previously demonstrated to substantially improve stability characteristics of bilateral teleoperators with communication delays; however, the transient response of the PBFR algorithms suffers from relatively slow force convergence. As a result, the high-frequency component of the reflected force is lost during the initial phase of contact with the environment, which has a strong negative effect on the haptic perception of the environmental stiffness and texture. In this paper, a new type of PBFR algorithms are developed which solve the aforementioned problem. The new algorithms are based on the idea to separate different frequency bands in the force-reflection signal and apply the PBFR principle to the low-frequency component, while reflecting the high-frequency component directly. Both theoretical analysis and experimental results are presented; the results obtained confirm that the new algorithms fundamentally improve force convergence without a negative effect on stability of the teleoperator system with communication delays. [ABSTRACT FROM PUBLISHER]

We present a new approach to determining the imaginary axis eigenvalues of a matrix delay equation. With a full rank delay coefficient matrix, the approach requires computation of the generalized eigenvalues of a pair of matrices which are a quarter of the size used in currently known matrix-based or operator approaches. These matrices have square of n for both row and column length, improved from twice those lengths, for an equation having matrix n × n coefficients with rank n delay matrix. Considering problem dimension and computational demands, this brings matrix-based approaches more in synchrony with the well-known scalar substitution approach. Given the symmetries evident in our approach, problems previously done with computation alone can now be considered with insight, and sometimes completed with simple calculations. Some of the computational and mathematical features of the approach are displayed in a section of examples. [ABSTRACT FROM AUTHOR]

We apply the stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on the dynamic programming principle, we characterize the value function as the unique viscosity solution of an associated Hamilton-Jacobi-Bellman variational inequality. We also provide a complete proof of the comparison principle which is the main assumption of the stochastic Perron's method. [ABSTRACT FROM AUTHOR]

In this study, both state feedback control and output feedback control design schemes are considered for a class of feedforward non‐linear systems with distributed delays. First, by using the state transformation of non‐linear systems, the problem of designing controller can be converted into that of designing a dynamic parameter, which is dynamically regulated by a dynamic equation. Then, the dynamic equation is delicately constructed by appraising the non‐linear terms of the given systems. At last, with the help of Lyapunov stability theorem, it is provided the stability analysis for the closed‐loop system consisting of the designed controller and the given systems. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. [ABSTRACT FROM AUTHOR]

This study is concerned with the non‐fragile H∞ control problem for a class of discrete‐time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite‐distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time‐delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non‐fragile H∞ output‐feedback controller such that the closed‐loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non‐fragile control problem is then recast as a convex optimisation problem solvable via the semi‐definite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

Resonant parts can be used in current controllers to suppress harmonics. However, they may cause destabilization of poorly damped grid and/or input-filter resonances, particularly for a nonnegligible converter time delay. This letter presents a design method whereby destabilization is prevented by making the converter's input admittance passive. [ABSTRACT FROM AUTHOR]