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This article considers the problem of finite-time command-filtered control for switched nonlinear systems with input quantization and output constraints. The unmeasurable state is estimated by designing a switched state observer. During the design process, to overcome the chattering problem effectively, the hysteresis quantization is designed as two bounded nonlinear functions. Furthermore, in order to restrict the output to an expected range, the barrier Lyapunov function approach is introduced. The "explosion of complexity" and the error compensation problems in the backstepping design are solved by using a finite-time command-filtered approach. A first-order Levant differentiator is used instead of the general command filter in this paper, which can not only filter the intermediate signals accurately to get the differential signals, but also ensure the finite-time stability of the filter. Stability of the closed-loop system in the sense of semi-global practical finite-time stability (SGPFS) is proved by exploring a multiple Lyapunov functions approach. Finally, a simulation example is provided to verify the validity of the presented control method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X.H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72–85] when 1< p i <2 for i =1,2,…, n. [Copyright &y& Elsevier]

Abstract: This paper considers certain neutral differential equation with the distributed delayWithout imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355–361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result. [Copyright &y& Elsevier]

This paper discusses the congestion control challenges in a network employing multi-bottleneck Transmission Control Protocol/Active Queue Management (TCP/AQM). The study specifically focuses on networks characterized by input nonlinearity and unknown disturbances. We regard the network as a whole, and consider the influence between multiple nodes and unknown disturbance, a dynamic model of multi-bottleneck network is established. And the impact of dead zone and saturation on the system is taken into account for the first time in the model, the builded TCP/AQM model is more practicable. Based on the characteristics of fuzzy logic systems (FLS), combined with backstepping technology and Lyapunov function, an adaptive congestion control algorithm is designed to make full use of the link resources of each node and improve the network utilization. Ultimately, the proposed algorithm's efficacy and superiority are substantiated through simulation. [ABSTRACT FROM AUTHOR]

Correction to the articles "Stability of Nonlinear 2D Systems Described by the Continuous-Time Roesser Model" and "Stabilization of Differential Repetitive Processes" published in the previous issue of the journal is presented.

This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the threshold dynamics of impact media reaction diffusion system is also given and the Kuratowski measure κ of non-compactness is also considered. In addition, assume the spatial environment is homogeneous, it is shown that the unique endemic equilibrium of the system is global stability by constructing suitable Lyapunov function. Finally, we discuss the asymptotic profile of the system when the diffusion rate of the susceptible (infected) individuals for the system tends to zero or infinity. The main results show that the activities of infected individuals can only be at low risk, and then the virus eventually will be extinct, that is, to control the entry of viruses from abroad and increase the detection of domestic viruses. Finally, some numerical simulations are worked out to confirm the results obtained in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a stability analysis and the controller improvement of T-S fuzzy Descriptor system are studied. Firstly, by making full use of the related theory of fuzzy affiliation function and combining the design method of fuzzy Lyapunov function with the method of inequality deflation, a stability condition with wider admissibility and less system conservatism is proposed. The advantage of this method is that it is not necessary to ensure that each fuzzy subsystem is progressively stable. We also maximise the boundary of the derivatives of the affiliation function mined. Secondly, a PDC controller and a Non-PDC controller are designed, and the deflation conditions for the linear matrix inequalities of the two controllers are constructed. Finally, some arithmetic simulations and practical examples are given to demonstrate the effectiveness of the method studied in this paper, and the results obtained are less conservative and have larger feasible domains than previous methods. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic tracking problem for a class of second-order electromagnetic micromirror model with output performance constraints and anomaly control, which is subject to model parameter uncertainties and external disturbances. Specifically, this paper formulates the trajectory tracking control problem of an electromagnetic micromirror as a closed-loop control trajectory tracking problem based on the general solution framework of output regulation. Moreover, the extended internal model is introduced to reformulate the closed-loop control problem into a state stabilization problem of the augmented system. Based on the augmented system, an internal model backstepping controller is proposed by integrating the barrier Lyapunov Functions (BLF) and the Nussbaum gain function with the backstepping structure.This controller not only satisfies the output performance constraints of the micromirror, but also maintains the control performance in anomalous control situations. The final performance simulation demonstrates the efficacy of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, some less conservative sufficient conditions for uniform exponential stability, local uniform exponential stability and uniform practical exponential stability of nonlinear time-varying systems on time scales are proposed. Compared with the traditional exponential stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. The main tools used are some Gronwall's inequalities on time scales. Two examples are also included to verify the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of spacing control between adjacent trains in train formation and proposes a distributed train-formation speed-convergence cooperative-control algorithm based on barrier Lyapunov function. Considering practical limitations such as communication distance and bandwidth constraints during operation, not all trains can directly communicate with the leader and obtain the expected trajectory it sends, making it difficult to maintain formation consistency as per the predetermined ideal state. Furthermore, to address the challenge of unknown external disturbances encountered by trains during operation, this paper designs a distributed observer deployed on each train in the formation. This observer can estimate and dynamically compensate for unknown reference trajectories and disturbances solely based on the states of adjacent trains. Additionally, to ensure that the spacing between adjacent trains remains within a predefined range, a safety hard constraint, this paper encodes the spacing hard constraint using barrier Lyapunov function. By integrating nonlinear adaptive control theory to handle model parameter uncertainties, a barrier Lyapunov function-based adaptive control method is proposed, which enables all trains to track the reference trajectory while ensuring that the spacing between them remains within the preset interval, therefore guaranteeing the asymptotic stability of the closed-loop system. Finally, a practical example using data from the Guangzhou Metro Line 22, specifically the route from Shiguang Road Station to Chentougang Station over three stations and two sections, is utilized to validate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time boundedness problem of switched linear systems under periodically intermittent control. Sufficient conditions are established to guarantee finite-time boundedness or finite-time stability of switched linear systems under periodically intermittent control. The proof procedures are implemented successfully resorting to piecewise Lyapunov functions. Based on the linear matrix inequality technique, the conditions are casted into a convex optimisation problem and therefore, they can be efficiently handled. The method proposed in this paper is a much potentially useful one in practice because of its economical and efficient nature that is easy to employ. Finally, two examples are given to express the validity and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive consensus with limited information for a class of uncertain nonlinear multi-agent systems (MASs). The limited information, meaning the incomplete information transmitted between agents, stems from nonzero-kernel weight matrices of communication networks, which deserves concerns owing to its practical interest such as in privacy preserving and information compression. Apart from the limited/incomplete information, the paper considers nonlinear MASs with large uncertainties (without known upper bounds). This is essentially different from the existing results of linear systems and poses challenges for the design and analysis of adaptive consensus. As for fully distributed protocol design, dynamic high gains are introduced to compensate for the system uncertainties and for the unavailable global graph information. In closed-loop consensus analysis, a new Lyapunov function is constructed by utilising weight and incidence matrices instead of Laplacian matrix. It turns out that the designed protocol can guarantee the boundedness of closed-loop MASs signals and the convergent consensus. Two numerical examples are given to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different Φ-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the fractional exponential stability of bidirectional associative memory (BAM) neural networks with conformable derivative. Applying the contraction mapping theorem existence and uniqueness of the equilibrium is studied. Furthermore, an appropriate Lyapunov function is stated to get exponential stability. Numerical examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This survey paper complements to our previous review papers on Lyapunov-type inequalities and contains some of the most recent results on these inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions. In precise terms, we have included the results related to Riemann-Liouville, Caputo, mixed Riemann-Liouville and Caputo, Riesz-Caputo, ψ -Caputo, Hadamard, Katugampola, Hilfer, ψ - Hilfer, proportional, variable order Hadamard, partial, systems of Riemann-Liouville, bi-ordinal Hilfer-Katugampola, and ψ -Hilfer fractional derivative operators. The Lyapunov-type inequalities for discrete fractional boundary value problems are also presented. [ABSTRACT FROM AUTHOR]

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when Δ < 0 ( Δ appears in Section 3), the three classes I t , M t , and R t appearing in the model go extinct at an exponential rate, and the susceptible class S t almost surely converges to the solution of the boundary equation exponentially. When Δ > 0 , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of Δ = 0 under some conditions. Some examples were listed to confirm the obtained results. The dynamic behavior of a stochastic epidemic model with information intervention and vertical transmission was the concern of this paper. The threshold to judge the extinction and persistence of the disease was obtained. Specifically, when ( appears in Section 3), the three classes , , and appearing in the model go extinct at an exponential rate, and the susceptible class almost surely converges to the solution of the boundary equation exponentially. When , the result that the disease in the model is persistent in the mean and the existence of invariant probability measure are proved by constructing a new form of Lyapunov functions, which results in getting sufficient and nearly necessary conditions for different properties. Moreover, one of the main characteristics of this article was the study of the critical case of under some conditions. Some examples were listed to confirm the obtained results. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

This paper investigates the problem of exponential H ∞ output control for switching fuzzy systems, considering both impulse and non-impulse scenarios. Unlike previous research, where the average dwell time (ADT: τ a ) and the upper bound of inter-event intervals (IEIs: T) satisfy the condition τ a ≥ ln μ + (α + β) T α = ln μ + β T α + T , implying that frequent switching is difficult to achieve, this paper demonstrates that by adopting the mode-dependent event-triggered mechanism (ETM) and a switching law, frequent switching is indeed achieved. Moreover, the question of deriving the normal L 2 norm constraint is solved through the ADT method, although only a weighted L 2 norm constraint was obtained previously. Additionally, by constructing a controller-mode-dependent Lyapunov function and adopting logarithmic quantizers, the sufficient criteria of exponential H ∞ output control problem are presented. The validity of established results is demonstrated by a given numerical simulation. [ABSTRACT FROM AUTHOR]

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 discusses the synchronization problem of impulsive stochastic bidirectional associative memory neural networks with a diffusion term, specifically focusing on the fixed-time (FXT) and predefined-time (PDT) synchronization. First, a number of more relaxed lemmas are introduced for the FXT and PDT stability of general types of impulsive nonlinear systems. A controller that does not require a sign function is then proposed to ensure that the synchronization error converges to zero within a predetermined time. The controllerdesigned in this paper serves the additional purpose of preventing the use of an unreliable inequality in the course of proving the main results. Next, to guarantee FXT and PDT synchronization of the drive–response systems, this paper employs the Lyapunov function method and derives sufficient conditions. Finally, a numerical simulation is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the finite-time stability and applications of positive switched linear delayed systems under synchronous impulse control, which includes two types of random switching and average dwell time switching. By constructing a type of linear timevarying co-positive Lyapunov functional, we first propose several new finite-time stability criteria. It should be emphasized that the linear term coefficient of the linear vector of the Lyapunov functional is adjusted to the difference between the weighting vector and the given vector. Then, we apply the obtained stability criteria to the linear time-varying delayed systems with impulsive effects. At last, three examples are given to demonstrate the validity of the obtained results, which includes the specific linear programming algorithm process. [ABSTRACT FROM AUTHOR]

For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader's attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient "few controlling many" paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. [ABSTRACT FROM AUTHOR]

In this paper, the asynchronous control problem is investigated and a multiple convex Lyapunov functions (MCLF) approach is introduced for a class of discrete-time switched linear systems under the Φ-dependent integrated dwell time (ΦDIDT) switching strategy. For the problem of asynchronous switching, this paper considers that Lyapunov functions may jump when the subsystem switches or the controller changes. Thus, the constructed MCLF is dependent on both the asynchronous interval and the synchronous interval, and the synchronous interval is divided into the convex interval and non-convex interval parts. Some sufficient conditions of stability with Linear matrix inequality (LMI) forms are obtained, and the asynchronous controller is designed to guarantee the globally uniform exponential stability of the system under study. In addition, the proposed method can degenerate to the existing methods to deal with the asynchronous control problem. Finally, a numerical example illustrates the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the switching topologies and tracking agent replacements for a class of nonlinear multi-agent systems with external disturbances. In particular, it is assumed that a number of monitoring agents are randomly deployed in a two-dimensional space. The agents are committed to tracking any intrusion targets in this area. When one of the following agents exits tracking for some reasons, the agent closer to the target joins the tracking team to ensure the number of tracking agents does not change. In order to achieve the successful tracking of the target, this paper designs a sliding mode controller for the relay multi-agent system with tracking agent replacements. Furthermore, an adaptive law is proposed to estimate the upper bound of disturbance in the relay tracking process. Next, the stability of the overall system will be analysed by applying the multiple Lyapunov function method based on the average dwell time. Finally, the effectiveness of the tracking strategy is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies several problems related to quadratic matrix inequalities (QMIs), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, or bounded or has a nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured"" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMIs can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller and also leads to explicit formulas for data-guided feedback gains. [ABSTRACT FROM AUTHOR]

This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average l-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period l. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models. [ABSTRACT FROM AUTHOR]

This paper deals with the application of a fuzzy-logic-based controller for a drive with a BLDC motor. Two main aspects of the work are presented in this paper. The first of them is focused on the design process of the fuzzy model. For this purpose, the rules of the applied fuzzy system are defined according to the Lyapunov function. The gain coefficients of the controller are optimized using the Chameleon Swarm Algorithm. Various issues and aspects were analyzed in the simulation tests (robustness against parameter changes, the influence of the controller parameters on the precision of control, stages of optimization, etc.). The presented work confirms the assumptions regarding precision and stable operation (also in the presence of changes in the object parameters—the mechanical time constants of the engine) in connection with the applied fuzzy speed controller. Moreover, the second part of the manuscript presents the low-cost power electronic device developed for laboratory tests. It uses STM32 ARM-based microcontrollers (state variable measurement, control algorithm calculation, control signal generation) and a Raspberry Pi 4B microcomputer (control application—reference value and parameter definition). The experiment performed for the control structure—an electric drive with a BLDC motor—verified the theoretical considerations. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability. [ABSTRACT FROM AUTHOR]

In this paper, the tracking control problem of the fully actuated rigid body system defined on the matrix Lie groups with impulsive effects is considered. By embedding the impulsive control systems defined on manifolds into Euclidean space via a feedback integrator, we obtain sufficient conditions for the invariance and attractivity of the manifolds. Then the embedding technique is applied to the fully actuated rigid body system with impulsive effects. The study of such a system with impulsive effects can be divided into impulsive disturbance problems and impulsive control problems, both of which are addressed in this paper. In the presence of impulsive disturbances, we realize the tracking target by the Lyapunov functions as well as the generalized Barbalat's Lemma. For the impulsive control problem, a controller containing impulsive input is designed for tracking control based on the high‐order fully actuated system approach. Finally, several examples demonstrate the effectiveness of the results presented in this paper. [ABSTRACT FROM AUTHOR]

In this paper, finite-time and fixed-time function projective synchronization of competitive neural networks with time-varying delays and noise perturbation is studied. Firstly, different from the existing papers, a more flexible Lyapunov function is constructed based on p-norm and two hybrid controllers are designed in this paper. Secondly, based on the finite-time and fixed-time stability theory and stochastic analysis theory, some new and useful finite-time and fixed-time function projective synchronization criteria are obtained. Furthermore, the settling time is derived with the help of some lemmas and mathematical inequalities under the appropriate control scheme. Finally, illustrative examples are given to show the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study the absolute stability and H∞$$ {H}_{\infty } $$ control problem for switched Lurie system (SLS) under asynchronous switching. A novel Lyapunov‐Lurie function is constructed, which is discontinuous and allowed to increase at the switching instants and the instants when controller modes and system modes are matched. Considering the superiority of time‐varying Lyapunov function technique, this paper is concerned with the Lyapunov‐Lurie function with time‐varying characteristic. Then, based on the switched time‐varying Lyapunov‐Lurie function (STVLLF) and mode‐dependent minimum dwell time (MDMDT) method, some control synthesis conditions are derived. The developed controller can guarantee the absolute stability and L2$$ {L}_2 $$‐gain performance for the closed‐loop SLS with admissible switching lag. Subsequently, a time‐varying control scheme is proposed from the STVLLF. H∞$$ {H}_{\infty } $$ control synthesis conditions in terms of linear matrix inequalities are established, which improve the existing results. Finally, two numerical examples are considered to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The dynamics of the propagation and outspread of infectious diseases are eminently intricate, mainly due to the heterogeneity of the host individuals. In this paper, an age‐stratified SEIR (susceptible‐exposed‐infected‐recovered) epidemiological model incorporating saturated treatment function and heterogeneous contact rates is developed to study infectious disease transmission dynamics among various age groups. The expression for the basic reproduction number R0$$ {R}_0 $$ and conditions for the global stability of the system have been derived by a recently developed graph‐theoretic (GT) approach. Digraph reduction creates a GT version of the Gauss elimination method for computing the R0$$ {R}_0 $$. The global dynamics results have been formed by constructing the Lyapunov function using a GT approach. The endemic equilibrium exists uniquely if R0>1$$ {R}_0>1 $$, whereas the disease‐free equilibrium is observed to be globally stable if R0≤1$$ {R}_0\le 1 $$. The numerical simulations are demonstrated by extracting the daily reported COVID‐19 cases for the second wave in Italy. The age‐dependent contact matrix for the Republic of Italy (data sourced from the POLYMOD study) is computed via paper–diary methodology (PDM) grounded on a population‐prospective survey in European countries. Our numerical findings imply that (i) for the age group (20–49) years and (50–69) years, the number of infected persons is quite double as compared with the exposed cases; (ii) approximately 50% of positive cases lies in (20–69) years age group; (iii) for the (00–19) years age group, only half of the exposed individuals got infected; and (iv) a consistent graph is detected for the age group of (70–99) years in both cases; it shows that almost all the exposed got infected. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive radial basis function neural network (RBFNN) is investigated and presented for identifying the nonlinear dynamical system. In traditional RBFNN structure, the selections of the activated radius are decided by the designer's experience to satisfy the best approximation of nonlinear dynamical function. In order to reduce the experience error, an adaptive RBFNN mechanism that can realize auto-regulation of activated radius is proposed in this paper. Taking the lattice points as the center of activated function, we use Taylor expansion to separate the factor of activated radius in local space. In order to ensure that the identification error has the property of fast convergence, the error conversion function is used for shrinking the gain in the error differential equation. Constructing a Lyapunov function to determine the differential equation of the weights and the activated radius, it is shown that the weights and the activated radius will converge to the neighborhood of its true value and the identification error will converge to neighborhood of zero in a periodic or period-like nonlinear dynamical system. To illustrate the effectiveness of the proposed adaptive RBFNN, Vanderpol and Duffing dynamical system are used as test examples, in comparison with traditional RBFNN and wavelet neural networks (WNN). The results show that the proposed method has best accurate identification and approximating effect in all of test algorithms. [ABSTRACT FROM AUTHOR]

The paper studies the design of interval observer–based event-triggered H ∞ controller for switched systems with frequent asynchronism. We first propose an interval observer–based event-triggered mechanism, which is used to transmit the observer states and the activated mode information for controller updating. Then, we design an interval observer–based event-triggered H ∞ controller for the considered systems. By using the controller mode–dependent Lyapunov function method, sufficient conditions for the globally exponential stability of the closed-loop switched systems are obtained under average dwell time switching law. Moreover, we prove that the interevent interval length is a positive constant, which can exclude the Zeno behavior. Compared with the literature, the paper removes the strict requirement of at most one switch between two event-triggered instants, that is, frequent switches within an interevent interval are allowed. Finally, a numerical example is given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The theory of compact global attractors for dynamical systems relies on the existence of a bounded absorbing set. In this paper, suppressing this condition, we present sufficient conditions to ensure the existence and uniqueness of maximal attractors for dynamical systems (both autonomous and nonautonomous). Such attractors are, in general, unbounded. For semigroups satisfying these conditions, when a Lyapunov function exists, we also present the characterization of the unique maximal attractor as the unstable set of the critical elements (not necessarily fixed points). As an example we present a semilinear parabolic equation to illustrate the theory in the autonomous case. For the nonautonomous setting, applying the general theory, we present an abstract evolution equation and a concrete parabolic equation as examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions. [ABSTRACT FROM AUTHOR]

This paper studies the combinatorial Calabi flow for circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. By using a Lyapunov function, we show that the flow exists for all time and converges exponentially fast to a circle pattern metric with prescribed attainable curvatures. This provides an algorithm to search for the desired circle patterns. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the fault-tolerant control problem for vehicular platoons with time-varying actuator fault directions and distance constraints. A bias constraint function is introduced to convert the asymmetric constraints into symmetric ones, based on which a unified barrier Lyapunov function (BLF) method is proposed to ensure distance constraints. Further, an adaptive fixed-time fault-tolerant controller in the context of a sliding mode control technique is proposed, wherein a new Nussbaum function is adopted to address the effects of unknown time-varying actuator fault directions. It is proved that both individual vehicle stability and string stability can all be guaranteed, and the effectiveness of the proposed algorithm is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R 0 s > 1 , then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R 0 s > 1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and φ < 0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler–Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R 0 s . Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue. [ABSTRACT FROM AUTHOR]

This paper explores the group consensus problem of second-order multi-agent systems (MAS) under asynchronous denial-of-service (DoS) attacks. Asynchronous DoS attacks involve the interruption of certain communication links, allowing the MAS to be reimagined as a switching system with a persistent dwell time (PDT). The agents in each group can be divided into three types, which are inter-act agents, intra-act agents with zero in-degree, and other agents. Then, according to the properties of the different agents, suitable agents are pinned. By leveraging the concepts of switching topology and the PDT, a suitable event-triggered control protocol is designed, along with the establishment of conditions to ensure the group consensus of the MAS. Moreover, through the construction of topology-dependent Lyapunov functions, the achievement of group consensus within the MAS under asynchronous DoS attacks is demonstrated. Subsequently, a numerical example is presented to validate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method. [ABSTRACT FROM AUTHOR]