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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]

In this paper, asymptotic stabilization problem for a class of nonlinear systems with unknown time‐varying delays is addressed. With the introduced static gain functions and new Lyapunov–Krasovskii functionals, a novel output feedback control strategy is developed. A memoryless output feedback controller which does not need precise knowledge of time delays is designed. The asymptotic stabilization and the boundedness of the closed‐loop system are proved via Lyapunov analysis. Finally, numerical simulation validates the effectiveness of this method for the nonlinear time‐delay system. [ABSTRACT FROM AUTHOR]

In this study, a sampled‐data networked control system over a multipath routing‐enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event‐driven strategy on the actuator side and the control policy on the decision‐maker side. The contributions of this study are twofold. First, by pre‐defining an application time as an event‐triggering parameter, the sampled‐data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F(⋅) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F(⋅) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F(⋅) and system parameters. [ABSTRACT FROM AUTHOR]

The problem of adaptive neural networks (NNs) control for a class of uncertain non‐linear systems with input delay and disturbances is studied. By using Pade approximation method, an auxiliary system is constructed to compensate the input delay based on the introduced variable. NNs are used to approximate the unknown non‐linear functions. With the aid of backstepping technique, adaptive NNs controllers are designed which can guarantee all the signals in the closed‐loop systems are semi‐globally uniformly ultimately bounded and the tracking error can be adjusted around the origin with a small neighbourhood. The stability of the closed‐loop systems is proved by using the Lyapunov stability theorem and two simulation examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy neural network (FNN) control scheme is proposed for a marine vessel with time‐varying constraints, guaranteed transient response and unknown dynamics. A series of continuous constraint functions are introduced to shape the motion of a marine vessel. To deal with the constraint problems and transient response problems, an asymmetric time‐varying barrier Lyapunov function is designed to ensure that the system states are upper bounded by the considered constraint functions. FNNs are constructed to identify the unknown dynamics. Considering existing approximation errors when FNNs approximating the unknown dynamics, an adaptive term is designed to compensate the approximation errors in order to obtain accurate control. Via Lyapunov stability theory, it has been proved that all the states in the closed‐loop system are uniformly bounded ultimately without violating the corresponding prescribed constraint region. Two comparative simulations are carried out to verify the effectiveness of the proposed control. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate the problem of finite‐time output regulation for a class of mismatched uncertain n ‐dimensional integrator, in which only the output signal is measurable and the higher derivatives of the matched and mismatched disturbances are bounded by time‐varying functions. Based on a finite‐time extended state observer, an output feedback controller is constructed. It is shown that even in the presence of mismatched uncertainties, whose high‐order derivatives are bounded by positive functions, the output of the system can be regulated to zero in finite time without requiring the knowledge of full‐state signals. An application to mass‐spring mechanical systems is given to illustrate the effectiveness and attractive properties of the authors' proposed controller. [ABSTRACT FROM AUTHOR]

This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag–Leffler stable if there is a convex and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation. [ABSTRACT FROM AUTHOR]

This study considers the adaptive neural backstepping control for multiple‐input and multiple‐output pure‐feedback systems subject to input saturation and disturbances. Neural networks are used to approximate the uncertain non‐linear functions without any prior limited conditions. A non‐linear disturbance observer and a state observer are constructed to design the output‐feedback neural controller. A new coordinate transform is defined to handle the pure‐feedback systems in the backstepping procedure. The proposed controller can make sure that all the state trajectories are ultimately bounded in the pure‐feedback non‐linear systems. An illustrative example is given to show the usefulness of the authors' designed new control method. [ABSTRACT FROM AUTHOR]

This study deals with adaptive control of non‐linear systems in the strict‐feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time‐varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed‐loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods. [ABSTRACT FROM AUTHOR]

This study is concerned with the non‐fragile mixed ℋ∞ /l2 − l∞ synchronisation control problem for discrete‐time complex networks with Markov jumping‐switching topology under unreliable communication links. The network topology under consideration is assumed to be governed by a Markov chain with time‐varying transition probabilities (TPs). The variation of TPs is subject to a kind of slow switching signals; that is, the average dwell time (ADT) switching. The focus is on the design of non‐fragile mixed mode‐dependent/‐independent controllers such that the underlying network reaches stochastic mean‐square synchronisation with a mixed ℋ∞ /l2 − l∞ performance level for an admissible switching signal with ADT. By using a new mixed ℋ∞ /l2 − l∞ performance index, combined with the switched control method, the solutions to the considered problem are formulated. Finally, simulation results demonstrate the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]