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This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the aperiodic sampling stabilisation problem for a class of switched linear systems under asynchronous switching. Based on a novel dynamic sampling rule, a sampling-point-based partition-dependent discontinuous Lyapunov functions control approach are developed to make the considered closed-loop switched systems be globally asymptotically stable. Compared with the existing results, the proposed control method permits frequent switching in a sampling interval for subsystems. But the frequent information transmission to the matched controllers and the negative effect of long asynchronous running on system performance can be nicely handled in this paper. Moreover, the partitioned Lyapunov functions are allowed to increase in some segments of the synchronous operating intervals. Tighter synchronous duration and switching number which are determined by more than affine functions make the switching signal more flexible. Finally, simulation analyses of two examples show the advantages of the developed control strategy. [ABSTRACT FROM AUTHOR]

This paper deals with integral control of a class of switched affine systems characterised by time-varying differential equations that, along with the discontinuities caused by the switching, also depend periodically on an exogenous parameter, which is an affine function of time. The goal is to design a state-dependent switching function with integral action that ensures global asymptotic tracking of a trajectory of interest. The integral action is responsible for providing robustness to the system against uncertainties and load variations, whenever the discrepancy between the model and the real system is sufficiently bounded. Due to the integrator, all the convex combinations of the dynamic matrices are non-Hurwitz. In this case, the main difficulty is to guarantee that the time derivative of the Lyapunov function is strictly negative definite, which is done by means of LMIs and conditions on the affine terms. To the best of our knowledge, this is the first Lyapunov-based switching rule with integral action able to ensure global asymptotic tracking of a pre-specified profile. When applied to AC circuits the advantage is to design the switching rule based on the original system, without resorting to averaged models. The theory is illustrated by the control of a three-phase AC-DC converter. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of attitude trajectory tracking of rigid bodies subject to external disturbances. The attitude control problem has been studied in the last decades and novel solutions have been proposed. Nevertheless, most of the proposed controllers only achieve local or almost global asymptotic stability without considering external disturbances. Contrary to other works, we focus on the problem of achieving almost global exponential stability of the attitude tracking errors in the presence of external disturbances using continuous control laws. We propose an attitude trajectory tracking controller based on the exponential coordinates of rotation in combination with a disturbance observer that estimates the exogenous signals. To solve this problem, we adopt a hierarchical approach, where the proposed control law is divided into a kinematic controller (outer control loop) and a velocity tracking controller (inner control loop). To design the disturbance observer, it is assumed that exogenous signals can be generated by a linear exosystem, i.e. the magnitude and phase of the disturbance are unknown. The almost global exponential stability of the closed-loop dynamics' equilibrium point was proved by a strict Lyapunov function. The performance of the proposed approach is assessed by numerical simulations and experimental tests on a low-cost quadrotor. [ABSTRACT FROM AUTHOR]

This paper addresses the $ H_{\infty } $ H ∞ static output feedback control of discrete-time semi-Markov jump systems (S-MJSs) with mismatched modes in finite-time horizon. Different from the existing relevant work, transient dynamics in short-time is focused instead of the Lyapunov stability over infinite-time horizon. Considering the immeasurable system states, output control strategy is developed subject to mismatched modes. Firstly, S-MJSs in closed-loop form are established by designing a hidden mode-dependent output feedback controller. Based on the closed-loop system (CLS), new Lyapunov function relies on both system mode and elapsed-time are created, according to which fresh analysis criteria ensuring FTB and $ H_{\infty } $ H ∞ FTB are derived. To circumvent the non-convex difficulty arising in controller design, a separation technique is introduced such that the design prerequisites are obtained from the above performance analysis conditions. Finally, the boost converter circuit and a numerical example are borrowed to test the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers a design problem of adaptive gain robust model-following/tracking controllers for a class of uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions. The parameters for dead-zone characteristics are assumed to be unknown, and an adaptive dead-zone inverse method is applied so as to reduce the effect for dead-zone non-linearities. Moreover, for the purpose of reducing the effects of matched and mismatched uncertainties, compensation inputs are introduced. The proposed adaptive gain robust model-following/tracking controller can achieve that the tracking error asymptotically converges to zero. In this paper, by using piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed adaptive gain robust model-following/tracking controller. Finally, an example is given to demonstrate the effectiveness of the proposed controller design method. [ABSTRACT FROM AUTHOR]

Control and synchronisation of chaotic systems have received much attention due to their various potential applications. In this paper, the predefined-time master–slave synchronisation of two chaotic systems is investigated. With the help of two different predefined-time stability theorems, two controllers are designed to achieve the predefined-time synchronisation of two nonidentical chaotic systems. Then based on inequality techniques and a Lyapunov function, some new sufficient criteria are obtained to ensure that two nonidentical chaotic systems achieve predefined-time synchronisation. Finally, numerical examples are given to show the effectiveness of our new results. [ABSTRACT FROM AUTHOR]

This paper studies model predictive control (MPC) with control barrier function to solve the stability and safety problems of switched systems subject to input and state constraints. Considering that the system state is unmeasurable and disturbed, an observer-based MPC $ H_\infty $ H ∞ method is adopted to estimate the system state and suppress disturbances. A cost function is designed to optimise the state and control input of switched systems by minimising its upper bound, and the optimisation problem is further transformed into a feasibility problem. Moreover, a control barrier function is introduced to constrain the controller gains, which ensures that the initial state of switched systems converges to the steady state without entering the specified unsafe region. Furthermore, a set of matrix inequality conditions is given to express the input and state constraints. Then, the Lyapunov function and average dwell time (ADT) approach are used to obtain sufficient conditions for the asymptotic stability of switched systems. Finally, two simulation examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we shall deal with stochastic singular difference equations (SSDEs) with delay. The aim of the paper is to study the solvability and stability of SSDEs with delay. It is difficult to investigate these properties for SSDEs with a delay because of the singularity of the leading coefficient matrix. An index-ν concept is derived for the solvability of these equations. Stability of SSDEs with delay is studied by using the method of Lyapunov functions and comparison principle. An example is given to illustrate the results. To the best of our knowledge, these results are novel for SSDEs with delay. [ABSTRACT FROM AUTHOR]

This paper will investigate the prescribed-time stabilisation problem for a class of nonlinear systems with state constraints. A recursive design algorithm is proposed to solve the prescribed-time stabilisation problem. Firstly, a barrier Lyapunov function (BLF) is employed and a time-varying coordinate transformation is utilised. Then, a modified method of L g V -backstepping is proposed, and a novel stabilising function by adding a fractional term proposed in this paper which is capable of decreasing the BLF to the origin within any desired settling time and then achieving the prescribed-time stabilisation. Such a fractional term plays an important role in achieving prescribed-time stabilisation. Next, the analysis of the prescribed-time stabilisation with state constraints is presented. Finally, an example shows the effectiveness of the proposed method. The feature of this paper is that the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Other is that the constraints of all the states are not violated. [ABSTRACT FROM AUTHOR]

In this paper, a trajectory tracking control strategy is proposed for multi-legged underwater robot in the presence of input saturation and full-state constraints. An anti-windup compensator is introduced to solve the input saturation problem, which can compensate for the saturation difference directly. Besides, the state constrains are addressed by a new state saturation function and the external unknown disturbances are solved by interval type-2 fuzzy neural network approximator. The dynamic surface control method combines with backstepping method is utilised to construct Lyapunov function. The control law and signals of the closed-loop system can be guaranteed to achieve semi-global uniform boundedness. Numerical simulations are presented to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control approach is developed for full-state constrained switched nonlinear systems that have actuator saturation, periodic disturbances and unknown control direction. To deal with the full-state constraints, the Barrier Lyapunov functions are introduced to limit the state variables within the corresponding constraint conditions. Meanwhile, the Fourier series expansion technology is employed to deal with unknown periodic disturbances and unknown nonlinear dynamics jointly. Additionally, a Nussbaum-type function is used in the controller design to cope with the and unknown control gain and input saturation. On the basis of the Lyapunov stability theory, it is demonstrated rigorously that all signals of the closed-loop system are uniformly ultimately bounded, and the proposed controller ensures that the tracking error is kept within a compact set close to zero. In the end, the validity of the designed control protocol is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the output regulation problem with prescribed performance for nonlinear lower-triangular systems. To achieve the transient prescribed performance, the output transformation technique and barrier Lyapunov function technique are introduced to solve the output regulation problem. The prescribed performance control scheme based on normal backstepping is constructed not only to restrict the output error of the closed-loop system keeping in a prescribed performance bound, but also to achieve that the output tracks a designed trajectory asymptotically. The effectiveness of the proposed method is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive finite-time impedance control strategy based on optimised backstepping (OB) technique is proposed for robotic manipulators subject to state constraints. The existing OB methods approximately solve the intractable Hamilton-Jacobi-Bellman equation by reinforcement learning (RL) with Bellman residual error, which has intricate actor-critic updating laws and persistence excitation requirement. To overcome this drawback, we construct the simplified RL updating laws by converting the problem to the solution of a positive-definite function, which is composed of actor-critic network weights. Then, the simplified RL updating laws can significantly reduce the controller complexity and relax the persistence excitation. Based on the barrier Lyapunov function, a barrier-type performance index function is constructed for the optimised controller under state constraints. The finite-time stability theory can guarantee the finite-time convergence property of the closed loop system without violating the prescribed constraints. Finally, we demonstrate the effectiveness of the proposed method in the simulation example with environment-robot interaction. [ABSTRACT FROM AUTHOR]

In this paper, the distributed mixed H 2 / H ∞ fusion filter design problem is investigated for a class of cyber-physical systems subject to non-ideal measurements under Round-Robin protocol. To save the limited communication resources, the Round-Robin protocol is employed to schedule the data transmissions from the sensors to the remote filters. The measurement is imperfect by taking into account the noises, the random saturations, nonlinearity perturbations and packet dropouts. The objective of this study is to propose a desired fusion filtering method that ensures the prescribed performance constraints on both the local and fusion filtering error dynamics. With the aid of Lyapunov function and stochastic analysis technique, a sufficient condition is established to guarantee the mixed H 2 / H ∞ performance index for the local filtering error systems, and then the filter parameter matrices are derived by resorting to the solutions to some matrix inequalities. Subsequently, on the basis of the obtained local state estimates, the proper fusion parameters are acquired by solving a convex optimisation problem. Finally, a numerical example is provided to demonstrate the effectiveness of the designed fusion filter. [ABSTRACT FROM AUTHOR]

This paper studies the problem of dynamic adaptive event-triggered synchronisation control for a class of complex dynamical networks (CDNs) with parameter uncertainty and stochastic network attacks. In order to save communication resources, reduce the driving burden and overcome the conservatism of fixed parameters, an improved event-triggered control strategy is designed. Firstly, a new synchronisation error model with uncertain of internal coupling weights between nodes and stochastic network attacks on actuator is modelled. Secondly, the Bernoulli stochastic distribution process is used to describe the probability of stochastic attacks, and the actuator failure model is adopted to depict actuator failure. By establishing an appropriate Lyapunov function, some sufficient conditions to ensure the asymptotic stability of the synchronisation error system is derived, which reduces conservatism. In addition, the cooperative design of controller and adaptive event-triggered strategy is solved by solving linear matrix inequality. Eventually, two examples are given to illustrate the effectiveness and potential of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper addresses novel discrete-time H 2 and H ∞ filter designs for polytopic linear parameter-varying (LPV) systems. A less conservative approach is employed to obtain the synthesis conditions, such that the polytopic LPV system state-space representation may have all its matrices subject to time-varying parameters and be solved by an efficient procedure. Parameter-dependent Lyapunov functions are used to derive both H 2 and H ∞ discrete-time filter design conditions resulting in a poly-quadratic approach in terms of linear matrix inequalities. A multi-objective H 2 / H ∞ solution is also provided. The proposed conditions have the advantage of recovering the established poly-quadratic concept as a particular case, which was an unresolved problem until the present paper. Moreover, using the addressed approach, it is possible to obtain improved quadratic H 2 and H ∞ filters. Numerical examples illustrate the proposed design methods applicability as an observer to estimate LPV system states and its performance in comparison with other approaches. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive finite-time tracking problem for nonlinear sandwich systems with dead-zone nonlinearity and full state constraints. The existence of the non-smooth dead-zone nonlinearity between the subsystems of the sandwich system makes the controller design as a challenging task. In this paper, a novel adaptive backstepping controller is proposed by employing the finite-time stability theorem and based on the barrier Lyapunov functions and finite-time command filters. The proposed controller guarantees the output tracking of the specified time-varying reference signal with the sufficiently small bounded tracking error in a finite-time. Moreover, all states of the controlled system are confined to predefined compact sets. To verify the theoretical achievements and show the applicability of the proposed method, simulation results are provided for both numerical and practical examples. [ABSTRACT FROM AUTHOR]

This paper studies adaptive finite-time control problem of a class of nonlinear systems with dynamic and parametric uncertainties. The power of systems in this paper is any positive odd rational number but not necessary equal to or greater than one. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterise the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, adding a power integrator, adaptive control and FTISS methods, an adaptive state feedback controller is designed to drive the states to the origin in finite time while maintaining all the closed-loop signals bounded. [ABSTRACT FROM AUTHOR]

In this paper, the problem of H2 and H∞ mixed switching control of uncertain discrete switched systems with time delay is considered via a switching signal design. New Lyapunov functional and Wirtinger inequality are used to guarantee the mixed performance for discrete switched time-delay system. The number of using LMI variables is less than our past proposed approach. Finally, a numerical example is illustrated to show the improvement of the developed results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of dynamic output feedback H ∞ control for continuous-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions without the special structure, a controller design method is developed and the relaxed stabilisation conditions are proposed. First, some shortcomings of the existing results are improved and a new approach is proposed for bounding the time derivatives of the membership functions. Then, less conservative conditions are obtained by introducing regulable parameters and applying the matrix decoupling techniques, which guarantee the prescribed H ∞ performance. Moreover, the relaxation technique proposed in this paper is also suitable for the fuzzy system with immeasurable premise variables. Finally, some examples are provided to demonstrate the validity of the approach. [ABSTRACT FROM AUTHOR]

This paper investigates the mixedH∞and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weightedH∞and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixedH∞and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given. [ABSTRACT FROM PUBLISHER]

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfyH∞filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper studies event-triggered based adaptive neural network (NN) tracking control of a robotic manipulator with output constraints and disturbance. First, a novel asymmetric tan -type barrier Lyapunov function (BLF) is developed to satisfy the requirement of time-varying output constraints. Then, a fixed threshold event triggering is proposed to reduce the energy consumption, which avoids the happening of Zeno behaviour after analysis. Further, a disturbance observer (DO) and an adaptive neural network are devised to estimate the bounded disturbance and the unknown dynamics of the robotic manipulator. The proposed controller can achieve uniform boundness of the solution and adjustment of transient performance. Finally, the effectiveness of the presented methods is verified by related simulation results. [ABSTRACT FROM AUTHOR]

This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well-known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the dynamical behaviours of a class of complex-valued neural networks with mixed time delays and impulsive effect. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for assuring the exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and mathematical induction method. The obtained results generalise the existing ones. Finally, two numerical examples with simulations are given to demonstrate the feasibility of the proposed results. [ABSTRACT FROM PUBLISHER]

This paper addresses the issue of reliable load frequency control design of an uncertain multi-area power system with constant time delays and disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which are described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the multi-area power system not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of global output feedback stabilisation for a class of uncertain nonlinear systems, where output function is time-varying and continuous, and multiple time delays exist in system state at the same time. A double-domination method is used to capture time-varying measurement error and delayed states. The control strategy is presented based on the choice of Lyapunov-Krasovskii functionals and the construction of a novel state observer without using the information on the output function and nonlinearities. A simulation example is given to show the efficiency of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of exponential stability in the sense of Lagrange for impulses in discrete-time delayed recurrent neural networks. By establishing a delayed impulsive discrete inequality and a novel difference inequality, combining with inequality techniques, some novel sufficient conditions are obtained to ensure exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks. Meanwhile, exponentially convergent scope of neural network is given. Finally, several numerical simulations are given to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper proposes a new fuzzy model predictive control approach for continuous-time nonlinear systems in terms of linear matrix inequalities (LMIs). The proposed approach is based on the Takagi-Sugeno fuzzy modeling, a quadratic Lyapunov function, and a sampled-data parallel distributed compensation controller with constant sampling time. The goal is designing the sampled-data controller such that at each sampling time, the stability of the closed-loop system is guaranteed and an infinite horizon cost function is minimised. The main advantage of the proposed approach is to eliminate the approximations induced from discretizing the original system and cost function upper bound minimisation. Consequently, a lower bound of the cost function is obtained and the performance of the proposed model predictive controller is improved compared to the recently published papers in the same field of interest. In addition, the Euclidean norm constraint of the control input vector is derived in terms of LMIs. To illustrate the merits of the proposed approach, the proposed technique is applied to a continuous stirred tank reactor system. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability of impulsive discrete-time systems with infinite delays. Some sufficient conditions are obtained to guarantee the exponential stability of the considered systems by employing Lyapunov functions together with Razumikhin technique. Finally, three numerical examples are given to illustrate the effectiveness and superiority of the obtained results. It is the first time that the exponential stability of impulsive discrete-time systems with infinite delays is studied, the obtained results complement some recent works. [ABSTRACT FROM AUTHOR]

This paper studies generation of robust periodic solutions in a class of nonlinear discrete-time system. The sustained oscillations, with the desired frequency and amplitude, are achieved through the creation of the appropriate elliptic limit cycle in the phase plane of the uncertain closed-loop discrete-time system. In the first step, the nominal control law is designed to enforce the trajectories of the nominal closed-loop system to converge to the desired limit cycle. Next, considering uncertain terms, an additional robustifying term is designed. This term is added to the nominal controller to sustain the desirable stable oscillations in the presence of uncertain terms. The resulted robust controller brings the trajectories of the uncertain closed-loop discrete-time system to a boundary layer (with adjustable width) around the desired limit cycle. Moreover, the domain of attraction of the limit cycle and also the ultimate boundary layer around it are calculated via the Lyapunov analysis. Additionally, in order to verify the applicability of the proposed method, it is implemented on the discretised model of a spring-damper system. Computer simulations confirm the theoretical results in generating robust stable oscillations. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of full state constraints-based adaptive control for a class of switched nonlinear pure-feedback systems under arbitrary switchings. First, the switched pure-feedback system is transformed into a switched strict-feedback system with non-affine terms based on the mean value theorem. Then, by exploiting the common Lyapunov function (CLF) method, the Barrier Lyapunov function method and backstepping, state feedback controllers of individual subsystems and a common Barrier Lyapunov function (CBLF) are constructed, which guarantee that all signals in the closed-loop system are global uniformly bounded under arbitrary switchings, and full state constraints are not violated. Furthermore, the tracking error can converge to a bounded compact set. Two examples, which include a single-link robot as a practical example, are provided to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of delay-dependent robust stability for singular time-delay systems is investigated. The parametric uncertainties are assumed to be norm bounded. Based on the idea of delay partitioning, A new Lyapunov-Krasovskii functional is proposed to develop new delay-dependent criteria, that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, some numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous works. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of non-smooth state feedback control for a group of high-order p-normal form interconnected nonlinear systems with prescribed performance. Each subsystem is in the form of triangular structure with the unmodelled dynamics. With the help of appropriate Lyapunov function, a state feedback controller is constructed via backstepping method. It is strictly proved that the closed-loop system is asymptotically stable and both transient and steady-state performances of the outputs are preserved. Finally, simulation results are presented to illustrate the effectiveness of proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of cooperative state estimation of general linear multi-agent systems subject to heterogeneous bounded external disturbances. This problem specifies the objective that each agent estimates its own state by using only relative information from its neighbours. Because of the existence of external disturbances, the problem is challenging especially when stringent exact estimation performance is desired. To this end, two cooperative estimation protocols are proposed, including the discontinuous nonlinear protocol for exact state estimation and the continuous nonlinear protocol for estimation with bounded errors. The overall network stability and convergence properties are analysed using the Lyapunov function method. A simulation example has also been used to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive neural network asymptotical tracking is investigated for a class of nonlinear system with unknown function, external disturbances and input quantisation. Based on neural network technique, an adaptive asymptotical tracking controller is provided for an uncertain nonlinear system via backstepping method. In order to reduce complexity of the control algorithm in the backstepping design process, a sliding mode differentiator is employed to estimate the virtual control law and only two parameters need to be estimated via adaptive control technique. The stability of the closed-loop system is analysed by using Lyapunov function method and zero-tracking error performance is obtained in the presence of unknown nonlinear function, external disturbances and input quantisation. Finally, an application example is employed to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of the delay-dependent filtering problem for a class of continuous-time singular Markov jump systems with Wiener process and generally uncertain transition rates (GUTRs). In the GUTR stochastic singular model under consideration, based on an auxiliary vector function, by employing an integral inequality and some appropriate free-weighting matrices, the delay-dependent sufficient conditions are derived, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, impulse-free and stochastically stable, but also satisfies a prescribed performance for all time-varying delays no larger than a given upper bound. Furthermore, the solvability conditions of the filtering problem are deduced in terms of a new type of candidate Lyapunov-Krasovskii function and a set of matrix inequalities. Finally, simulation examples are performed to validate the proposed method in this paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to design an adaptive controller for uncertain strict-feedback stochastic nonlinear systems with dead zone and input saturation. A barrier Lyapunov function in asymmetric forms is constructed which can relax the requirements for initial conditions. To simplify the design process of the controller, a dead zone-based model of saturation is implemented and neural networks are used to approximate uncertain nonlinear functions and to construct an observer to cope with difficulties raised by the presence of immeasurable state variables. By applying the backstepping technique, a smooth tracking controller with adaptive law is proposed to ensure all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Furthermore, the tracking error can converge to a small neighbourhood of the origin. The effectiveness of the proposed scheme is presented by simulations on a numerical example. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite-time H ∞ control for discrete-time switched linear systems via admissible edge-dependent switching. The admissible edge-dependent average dwell-time (AED–ADT) is employed to identify a class of constrained switching signals for the resulting closed-loop system. Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and H ∞ performance by incorporating the idea of AED–ADT. By constructing the MDLFs in quadratic forms, a synthesis condition for finite-time bounded control is first proposed, then a synthesis condition for finite-time H ∞ control is further developed based on the obtained result. Finally, two simulation examples are given to verify the effectiveness and practicability of the presented control synthesis method. [ABSTRACT FROM AUTHOR]

This paper deals with stabilisation, H 2 and H ∞ static output feedback synthesis, under structure constraints for linear time-invariant systems. The proposed approach relies on a prominent property of Hurwitz-stable matrices set and a Douglas-Rachford (DR) reflection method type for finding a point in the intersection of two closed sets. The method proposed in this paper emulates the genericity of the Linear Matrix Inequalities framework while keeping the feedback gain separated from any matrix with direct or indirect connection to the Lyapunov function. The link between the sequence of iterates generated by the proposed algorithm and a continuous dynamical system results in the use of Lyapunov stability theory for guaranteeing the local convergence. Several examples are given to prove the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we investigate the finite-time output feedback control issue for switched nonlinear systems. In the design procedure, fuzzy logic systems are used for identifying the unknown functions in switched nonlinear systems. A common state observer is constructed such that the unmeasured states can be measured. Based on the framework of the backstepping algorithm, an observer-based finite-time adaptive tracking control strategy is proposed via the common Lyapunov function approach. The stability analysis process confirms in detail that all the closed-loop signals are bounded under arbitrary switchings and the tracking error can converge to a small neighbourhood of the origin after a finite period of time. In order to verify the feasibility of the proposed control scheme, a numerical simulation example is shown in this paper. [ABSTRACT FROM AUTHOR]

In this paper, an integrated fault estimation (FE) and fault-tolerant control (FTC) method is proposed for linear parameter varying (LPV) systems using the parameter-dependent Lyapunov function. The observer-based estimation and fault-tolerant control structure causes an uncertainty between systems which is called the bi-directional uncertainty. Additionally, with simultaneous actuator and sensor faults, disturbances, the overall performance of the FTC system decreases. To maintain robust stability of closed-loop systems, an unknown input observer fault estimator approach with both state feedback control and sliding mode control is implemented as a solution by solving H ∞ optimisation using a linear matrix inequality (LMI) formulation. The efficiency of the integrated FE/FTC design is demonstrated using the pitch-axis missile LPV model and simulated to evaluate the merits of the suggested approach. [ABSTRACT FROM AUTHOR]

In the paper, some classes of time-varying nonlinear switched systems are considered. The stability problem is investigated. The Lyapunov direct method and the theory of differential inequalities are used. The non-stationary switched comparison equation with hybrid degrees is constructed for the considered system. Switching in the comparison equation can be caused by changing the operating modes, as well as changing non-stationary parameters of the system. Sufficient conditions of the asymptotic and finite-time stability are obtained. The region of attraction for the given equilibrium position is estimated. Some examples are presented to illustrate the results. In particular, some classes of nonlinear mechanical system are studied. [ABSTRACT FROM AUTHOR]

In this paper, we shall deal with stochastic singular difference equations (SSDEs) with constant coefficient matrices and nonlinear stochastic perturbations. The solvability and stability of SSDEs are difficult to study because of the singularity of the leading coefficient matrix. An index-ν concept is derived and formulas of solution are established for these equations. The continuous dependence of solution on initial condition is also considered. Finally, the stability of SSDEs is studied by using the method of Lyapunov functions. Some examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, a novel stability analysis method for continuous-time linear systems with aperiodic sampling is presented by using a partitioned looped-functional approach. Based on the Lyapunov function with a new looped-functional, the stability condition is derived by using a bidirectional fragmentation of a sampling interval from t k to t k + 1 , which is divided into two sides forward and backward directions based on time t. For the bidirectional regions, the new looped functional is constructed by taking into account relations between states defined at the fragmented time and the sampling time. The improvement using the proposed scheme is shown through the comparisons with existing methods. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered adaptive decentralised control strategy for a class of switched interconnected nonlinear systems is presented, which considers full-state constraints and unmodeled dynamics, simultaneously. In the controller design process, the approximation capability of radical basis function neural networks (RBF NNs) is used to estimate the unknown functions of the system. The interference caused by unmodeled dynamics is overcome by introducing a dynamic signal. In addition, the barrier Lyapunov function (BLF) is constructed for each subsystem to dispose the influence of state constraints. An adaptive control scheme with event-triggered mechanism is proposed to reduce communication burden. It is shown that the proposed event-triggered controller and an adaptive neural decentralised control strategy are designed such that all the signals in the closed-loop system are guaranteed to be bounded, the tracking errors of the system converge to a small neighbourhood of the origin and the full state constraints are not violated. Finally, a simulation result shows the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

In this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov-Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results. [ABSTRACT FROM AUTHOR]