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This article considers the problem of output feedback stabilization for a class of stochastic high‐order nonlinear time‐delay systems with unknown output function. For stochastic high‐order nonlinear time‐delay systems, based on the Lyapunov stability theorem, by combining the addition of one power integrator and homogeneous domination method, the maximal open sector Δ$\Delta$ of output function is given. As long as output function belongs to any closed sector included in Δ$\Delta$, an output feedback controller can be developed to guarantee the closed‐loop system globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

Aiming to improve the estimation and prediction accuracy of a target's position, this paper proposes a state estimation method for photoelectric tracking systems, based on the evaluation of the tracked target's motion intention. Traditional photoelectric tracking systems utilize external physical quantities such as the position, velocity, and acceleration of the target as the estimated states. While this method can output good results for pre‐modelled target positions, it struggles to maintain the accuracy when facing manoeuvering targets or complex motion patterns targets. Here, the relevant parameters of the tracked target's motion intention are directly estimated innovatively, like estimating the circling point position rather than the circular flying target's position and velocity. This approach enables recognizing the target's motion intention and leads to precise estimation, which specifically consists of an interacting multiple model approach, multiple unscented Kalman estimators, and a robust estimator. The effectiveness and stability of this estimator are validated through software simulations and experiments on a dual‐reflection mirror platform. [ABSTRACT FROM AUTHOR]

This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples. [ABSTRACT FROM AUTHOR]

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]

In this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval fractional‐order plants having an interval time delay. An interval fractional‐order plant is defined as a fractional‐order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D‐decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed‐loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional‐order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control (ADRC) has been gaining attention in recent years and has shown its performance in multiple applications including non‐linear ones, without the need of accurate models. Despite the good results of this technique, time delay can deteriorate the performance of ADRC, limiting its application. Here, the effect of time delay on the stability of a linear ADRC is analysed, using an alternative mathematical description, and a new effective design technique, based on a modified ADRC scheme, is proposed to overcome the delay effect while maintaining the disturbance rejection properties of the ADRC. An experimental example is discussed considering a system with low damped mechanical resonances, showing good results using the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, the operator spectrum theory is applied to study the general stabilisation issues for mean‐field stochastic Markov jump systems (MF‐SMJSs), where multiple delays, multiplicative noises and homogeneous Markov chain exist simultaneously. The innovative contributions are described as follows. On the one hand, a feasible model augmented strategy is adopted to transform the dynamics into an auxiliary delay‐free form. By introducing a delay‐dependent linear Lyapunov operator (DDLLO), the Lyapunov/spectrum stabilising conditions are constructed, which are both necessary and sufficient. On the other hand, in terms of spectral analysis technique, the notions of interval stabilisation and essential destabilisation are generalised to MF‐SMJSs for the first time. The necessary and sufficient stabilisation conditions are derived, respectively, which can be verified availably by LMI feasibility tests. To confirm the effectiveness of the theoretic results, two illustrative examples are included. [ABSTRACT FROM AUTHOR]

An improved robust stability surface analysis method is proposed in this study for fractional‐order time‐delay systems. Through the stabilisation process, a synthesised fractional‐order PD controller can be designed with guaranteed robustness specifications. Firstly, the specification for improved robustness requirements is proposed. In order to find selectable robust controller design parameter combinations for the controlled system, stability region is discussed based on the stability boundary locus, and the robust stability surface is derived straight after. Secondly, the selectable parameter combinations are checked to find the one that best fulfils all the proposed robustness specifications. Finally, numerical simulations are given to demonstrate the effectiveness and flexibility of the presented control algorithm. [ABSTRACT FROM AUTHOR]

This study isrelevant to the topic of a robust event‐triggered mechanism for the Takagi–Sugeno (T–S) fuzzy system with successive time‐delay (STD) signals and its application, where the uncertainties satisfy the randomly occurring form. Firstly, an event‐triggered communication scheme is introduced, which can adaptively adjust the communication threshold to save limited communication resource. The primary aim of this study is to model an event‐triggered mechanism with STD, which ensures that the suggested T–S fuzzy system achieves extended dissipative with permissible uncertainties. Secondly, by using the relaxed integral inequality technique, single and double auxillary function‐based integral inequalities to evaluate the derivative of the designed Lyapunov–Krasovskii functional, quadratically stable condition is established for the delayed fuzzy system in terms of linear matrix inequalities and analyse the H∞,L2−L∞, passivity, mixed H∞ and passivity, (Q,S,R)‐dissipativity execution by choosing the weighting matrices can be solved simultaneously in a standard framework based on the idea of extended dissipative. Finally, simulation studies are given to verify the effectiveness of the derived results, among them one example was supported by the real‐life application of the benchmark problem in the sense of STD signals. [ABSTRACT FROM AUTHOR]

This study addresses the gain‐scheduled control problem for discrete‐time delayed non‐linear parameter‐varying (NLPV) and linear parameter‐varying (LPV) systems. First, by constructing the parameter‐dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay‐dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay‐dependent linear matrix inequality conditions for the static output‐feedback control design and state‐feedback control design for delayed NLPV are provided. Second, the results obtained for discrete‐time delayed NLPV systems are modified in a simple way to deal with discrete‐time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The periodic event‐triggered control (PETC) and self‐triggered control (STC) for networked singular systems under denial‐of‐service (DoS) attack and deception attack are studied. Due to the fact that DoS attack is able to prevent the control input from transmitting and deception attack falsifies the control input as a non‐linear disturbance, a closed‐loop system is constructed with different control inputs based on the switched system method. Next, the attention is focused on the design of PETC and STC schemes. PETC scheme adopts the input delay approach to transform the closed‐loop system into a switched singular time‐delay system and adjusts the triggering intervals by the frequency and duration of cyber‐attacks. STC scheme relies on a reduced‐order system derived from the original singular system and utilises the current sampled information to predict the next triggering instant. Then, exponential stability criteria are derived by codesigning the triggering parameter and controller gain. Finally, a small‐signal version of the structure‐preserving power network model is given to demonstrate the effectiveness of the proposed methods. [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]

Actuator rate limit phenomenon is ubiquitous in control systems, but it has always been neglected in practical engineering. Especially, few papers are published to investigate the system identification while considering the rate limit. Step function is commonly used in parameter estimation and its first‐order derivative at the step time goes to infinity, which is not affordable by real actuators. As a result, the rate limit slows down the system response speed, misleads the parameter identification, and subsequently affects the controller design and deteriorates the control performance. This study proposes both graphical method and curve fitting method to identify the first‐order plus time‐delay (FOPTD) systems with consideration of the actuator rate limit effect whose limit value is unknown. Quantitative analyses of the parameter mismatch in the traditional FOPTD model and parameter sensitivity analyses are also carried out. Both simulation results and experimental results have shown the necessity and feasibility of defining a new model structure which includes the rate limit value. [ABSTRACT FROM AUTHOR]

This study tackles the problems of exponential stability analysis and model reduction for spatially interconnected discrete‐time systems with time‐varying delay. The well‐posedness, exponential stability, and contractiveness of spatially interconnected discrete‐time systems subject to time‐varying delay are defined and a sufficient condition in terms of linear matrix inequality (LMI) is put forth to test these properties. By exploiting the above analysis result, a sufficient condition for guaranteeing the existence of a reduced‐order system is derived. With the help of Finsler lemma, a reduced‐order system is derived based on the LMI method. By taking advantage of the same method, a delay‐free reduced‐order system for a given spatially interconnected discrete time‐varying delay system can also be attained. Finally, two examples have been carried out to show the feasibility and validity of the derived theories. [ABSTRACT FROM AUTHOR]

This study investigates the problem of fault detection (FD) filter design for a class of uncertain Lipschitz systems with time delays, unknown faults, parameter uncertainties and bounded disturbances. A novel FD filter is proposed and the augmented filter system is converted to a linear parameter varying (LPV) system by the reformulated Lipschitz property. Then, two bounded real lemmas (BRLs) are given for the generated residual signal to achieve the H− fault sensitivity performance in low‐/middle‐/high‐frequency domains and H∞ disturbance attenuation performance in the full‐frequency domain. Next, the obtained BRLs are further converted into a set of linear matrix inequalities (LMIs) to implement the filter design. Finally, two illustrative simulations including a numerical example and Chua's circuit system clearly demonstrate the advantages of the developed FD scheme. [ABSTRACT FROM AUTHOR]

This study is concerned with the robust model predictive control (MPC) based on recurrent multi‐dimensional Taylor network (RMTN) for the discrete‐time non‐linear time‐delay systems. Regarding the MPC algorithm for the discrete‐time time‐delay systems, the existing literature only considers the linear case. In this study, by designing the suitable terminal cost and terminal region, the MPC scheme is firstly investigated for the non‐linear case. Meanwhile, to reduce the computational burden of MPC using the existing model types (e.g. recurrent neural network) as the identified model, an RMTN possessing the concise structure and high computational efficiency is constructed to approximate the state‐space model of the system. After trained by the backpropagation through time algorithm, the RMTN obtaining the high accuracy of prediction over a long‐range horizon is capable of serving as the prediction model in the MPC scheme. Furthermore, aiming at alleviating the adverse effect of the inevitable identification error, the tube‐based MPC is proposed via leveraging dual‐mode MPC to guarantee that actual trajectory is contained within a robust tube. The stability of the considered system is proved theoretically, and numerical simulation is employed to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, optimal performance of the multi‐input multi‐output networked control systems (NCSs) is analysed. The systems are with a time‐delay and channel noise constraints in the forward network channel, and encoding–decoding and quantisation constraints, and packet dropouts in the feedback network channel. By using the Youla parameterisation of a two‐degree‐of‐freedom controller, a new and explicit expression of the optimal performance is derived. The optimal performance is obtained using the method of H2 norm technique. The results show that the positions and directions of the non‐minimum phase zeros and unstable poles of a given plant are related to the optimal tracking error. On the other hand, the optimal tracking error is dependent on channel noise, quantisation noise, encoding–decoding, time‐delay, packet dropout probability and other correction factors. Finally, simulation results demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

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]

This study addresses the problem of synthesising functional observers for positive time‐delay systems subjected to unknown inputs. A functional observer architecture for the problem is presented. The existence conditions of the observer and a linear programming problem characterising the existence conditions of such a functional observer are also established. An algorithm for designing the observer is presented. Finally, examples are given to showcase the effectiveness of the observer. [ABSTRACT FROM AUTHOR]

In this study, a polyhedral approximation method for reachable sets of linear delay systems is investigated. For a continuous linear system with multiple delays, the first Euler scheme combining with linear interpolation is used to transform it into a discrete one. Then a polyhedral approximation method based on optimisation techniques is proposed to compute the discrete reachable set. By specifying an approximation error and solving a finite number of convex optimisation problems, a polyhedron can be constructed as the approximation of the discrete reachable set. The approximation quality measured in Hausdorff distance can be directly controlled. Next, illustrated examples are given to demonstrate the effectiveness of the proposed method. Finally, the authors show some reachable sets of linear delay control systems, and they compare the proposed method with some other methods in the literature. Numerical results clearly show the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

This study addresses the non‐fragile controller design of a class of fractional‐order (FO) linear delayed systems assumed to have structured uncertainties in both the plant and the controller. By using the linear matrix inequality method, singular value decomposition and FO Razumikhin theorem, the delay‐dependent and order‐dependent robust non‐fragile state feedback controller and non‐fragile observer‐based robust state feedback controller are synthesised, respectively, based on whether the states are available or not. Three examples are presented to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This study focuses on the delay‐dependent robust exponential stabilisation and H∞ control for uncertain stochastic time‐delay systems with non‐linear terms. Uncertain parameters are assumed to be time‐varying norm bounded, while time‐varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method. [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 order to save the usage of system resources and adapt the variation of plant state, this study first proposes a novel stochastic‐sampling‐based adaptive event‐triggered scheme (AETS). Second, in the framework of time‐delay systems, the closed‐loop control system is modelled as a class of delayed stochastic systems where time‐delay is distributed in some intervals with probability. Then, by employing stochastic analysis tool and Lyapunov stability theory, a stability criterion for this class of delayed stochastic systems is established to ensure that the system possesses stochastically asymptotic stability with an H∞ disturbance attenuation performance. Also, a co‐design of parameter matrices of the state‐feedback controller and the stochastic‐sampling‐based AETS is implemented. Third, based on the obtained co‐design condition, a convex optimisation algorithm for the tradeoffs between disturbance attenuation performance and resource utilisation of the closed‐loop control system is further developed. Finally, the effectiveness and feasibility of the proposed control strategy are illustrated by two numerical examples of adaptive event‐triggered control for networked control systems under stochastic sampling. [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 discusses delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi‐sure exponential stability criteria for stochastic delay systems driven by G‐Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay‐free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G‐Lyapunov function. Some examples are introduced to illustrate the delay‐dependent stability criteria. [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]

This study presents a novel scheme for the synthesis of first‐order and super‐twisting sliding mode controllers for the robust stabilisation of a class of linear time‐invariant time‐delay systems subject to matched disturbances. Starting from a stability analysis of the system to guarantee that the resulting sliding mode dynamics is asymptotically stable, linear matrix inequality conditions of reduced conservatism are derived by using the Lyapunov–Krasovskii approach. Based on the stability analysis, the sliding mode controllers are synthesised to force the evolution of the closed‐loop system trajectories to converge onto a prescribed sliding surface and to ensure that they remain there for all subsequent time. Unlike existing results, the implementation of the proposed approach does not involve strong requirements on the system structure. A numerical and a practical example along with a comparative analysis prove the effectiveness of the proposal and highlight its benefits. [ABSTRACT FROM AUTHOR]

In this study, a new state‐dependent impulsive observer (SDIO) is proposed for a class of non‐linear time‐delay systems. The proposed observer is based on the extended pseudo‐linearisation technique that parameterises the non‐linear time‐delay system to a pseudo‐linear structure with time delay and state‐dependent coefficients. Applying this technique, the presented observer is utilised for non‐linear systems with multiple, time‐varying and distributed delays. Furthermore, the extended pseudo‐linearisation technique simplifies the procedure of impulsive observer design for non‐linear time‐delay systems. The proposed SDIO is capable of continuously estimating system states using discrete samples of the system output that are available at discrete impulse times. The stability and convergence of the proposed observer are proven via a theorem utilising time‐varying and delay‐independent Lyapunov function and the comparison system theory of impulsive systems. It is guaranteed that the estimation error asymptotically converges to zero under well‐defined and less‐conservative sufficient conditions that are presented in terms of feasible linear matrix inequalities. In addition, the stability theorem specifies an upper bound on the time intervals between consecutive impulses. Results are simulated on Congo Ebola disease model which is an epidemic non‐linear time‐delay system. Simulation results confirm the effectiveness and performance of the proposed SDIO. [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]

This study considers asymptotic stability in the mean square sense for stochastic delay Markovian reaction‐diffusion systems (SDMRDSs) via boundary control. Firstly, the authors present a boundary controller for the system. By constructing of a Lyapunov–Krasovskii functional and utilising of Poincaré inequality, a sufficient criterion of mean square asymptotic stability for SDMRDSs is established. Next, boundary control for stochastic Markovian reaction‐diffusion systems (SMRDSs) with time‐varying delays is also investigated, and a delay‐dependent sufficient condition for SMRDSs under the boundary control law is obtained. In addition, the robust boundary stabilisation of SMRDSs with parametric uncertainty is considered. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This study initially considers the relationship between stability radius and Lσ ‐gain of linear time‐invariant positive systems. The L1 ‐, L2 ‐, and L∞ ‐gains of an asymptotically stable positive system are characterised in terms of stability radii and useful bounds are derived. The authors show that the structured perturbation of a stable matrix can be regarded as a closed‐loop system with uncertainty structure represented by the unknown static output feedback. This makes it possible to relate the Lσ ‐gains in terms of closed‐form expression available for stability radii of Metzler matrices. The authors generalise the above connection for positive‐delay systems as well. Performance characterisation and computation of Lσ ‐gains are also given based on linear programming for σ=1,∞ and linear matrix inequality (LMI) for σ=2. The importance of this characterisation becomes evident when state feedback controllers are designed for regular and time‐delay systems with positivity constraints. In particular, they show that positive stabilisation with maximum stability radius for the case of σ=2 can be considered as an L2 ‐gain minimisation, which can be solved by LMI. This inherently achieves the performance criterion and establishes a link to the reported iterative convex optimisation approaches that have been developed for the cases of σ=1 and σ=∞. A significant result of this study is the derivation of bounds for Lσ ‐gains and the unique commonality among the optimal state feedback gain matrices in obtaining Lσ ‐gains of the stabilised system. [ABSTRACT FROM AUTHOR]

This study is concerned with the output feedback stabilisation problem for a class of large‐scale non‐linear time‐delay systems with unknown measurement sensitivities. The non‐linear terms are assumed to be bounded by states or delayed states multiplied by outputs polynomial functions. The state observers are given by the dynamic gain control design technique. By constructing an appropriate Lyapunov–Krasovskii functional, the global asymptotic stability of the closed‐loop control system is analysed. A numerical example is given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This study is concerned with resilient load frequency control (LFC) scheme design of multi‐area power systems with communication delay and aperiodic denial‐of‐service (DoS) attacks. First, to identify DoS attacks, a detection mechanism in the actuator side is proposed which is a time counter measuring the input delay. The identified DoS attacks are constrained by its upper bound of frequency and duration. When DoS attacks are identified, actuator switches to zero‐input strategy from hold‐input strategy. According to the switching control inputs, switched time delay system model is established to describe the attack influence on LFC system. Further, a criterion of preserving weighted H∞ performance is derived by combining piecewise Lyapunov–Krasovskii functional method with switched system method. Based on the criterion, the resilient control gain is designed by solving a set of LMIs. Finally, numerical simulations are given to verify the validness of the attack detection based resilient LFC scheme. [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]

Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete‐time systems with delay. By using the singular value decomposition approach, delay‐dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given. [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]

Distributed cooperative consensus tracking problem for a class of uncertain multi‐agent systems with a high‐dimensional leader under a directed communication topology is concerned. Compared with related works, the dynamics of the leader agent is allowed to be different from those of the followers and may not be measured. Meanwhile, the dynamics of each follower is subject to un‐modelled dynamics, unknown time‐varying delays, as well as external disturbances, which makes the model more suitable in various practical applications. Based on the M ‐matrix and Lyapunov–Krasovskii functional method, a distributed robust radial basis function neural network controller as well as a local observer is designed for each follower so as to guarantee the ultimate boundness of the tracking errors to the leader's output signals. By appropriately cutting down the neural network parameters to be updated online, the computational burden can be greatly reduced. The effectiveness of the proposed consensus approach is testified via a numerical example. [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 authors are interested in the mean square exponential stability of stochastic systems with variable and distributed delays. Different from the traditional methods, based on the well‐known Perron–Frobenius theorem and Itô formula, a proof by contradiction to explore some new criteria for the mean square exponential stability of stochastic delay systems is introduced. In particular, the proposed novel stability criteria reduce the traditional restrictions imposed on variable delays and also provide an optimal upper bound for delays. Two examples are given as applications to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This study provides an overview and in‐depth analysis of recent advances in stability of linear systems with time‐varying delays. First, recent developments of a delay convex analysis approach, a reciprocally convex approach and the construction of Lyapunov–Krasovskii functionals are reviewed insightfully. Second, in‐depth analysis of the Bessel–Legendre inequality and some affine integral inequalities is made, and recent stability results are also summarised, including stability criteria for three cases of a time‐varying delay, where information on the bounds of the time‐varying delay and its derivative is totally known, partly known and completely unknown, respectively. Third, a number of stability criteria are developed for the above three cases of the time‐varying delay by employing canonical Bessel–Legendre inequalities, together with augmented Lyapunov–Krasovskii functionals. It is shown through numerical examples that these stability criteria outperform some existing results. Finally, several challenging issues are pointed out to direct the near future research. [ABSTRACT FROM AUTHOR]

In this work, the problem of robust H∞ filtering for uncertain two‐dimensional (2D) continuous‐discrete Roesser systems with state delays in finite frequency ranges is investigated. This study first develops the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality. In particular, the proposed result covers FDIs in finite frequency intervals for 2D continuous/discrete/continuous‐discrete settings. Using the result, the existing finite frequency bounded ream lemmas and the finite frequency positive real lemmas have been generalised to uncertain 2D state‐delay Roesser systems. Then, a robust finite frequency H∞ filter design method for uncertain 2D continuous‐discrete state delay Roesser systems is given. Finally, examples are provided to clearly demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A reset methodology in controller design can affect the performance and stability of control systems. Stability of reset time delay systems can be addressed based on a similar theorem of Lyapunov–Krasoviskii theory. In this study, a robust delay‐dependent stability analysis of reset control systems is proposed for linear time invariant case. The conditions of stability are given in terms of linear matrix inequalities. In addition, extension of results is given to investigate stability of non‐linear reset systems. Numerical examples are used to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]