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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

The Jungle Game is used in population dynamics to describe cyclic competition among species that interact via a food chain. The dynamics of the Jungle Game supports a heteroclinic network whose cycles represent coexisting species. The stability of all heteroclinic cycles in the network for the Jungle Game with four species determines that only three species coexist in the long-run, interacting under cyclic dominance as a Rock–Paper–Scissors Game. This is in stark contrast with other interactions involving four species, such as cyclic interaction and intraguild predation. We use the Jungle Game with four species to determine the success of a fourth species invading a population of Rock–Paper–Scissors players. [ABSTRACT FROM AUTHOR]

Distribution-dependent stochastic differential equations (DDSDEs, in short), also called as McKean–Vlasov SDEs, are a special class of SDEs and have some concrete applications in mean-field control, mean-field games and complex networks. Stability plays fundamental role among the theory and applications for DDSDEs. In this paper, we discuss a class of distribution-dependent stochastic differential equations driven by time-changed Brownian motions (TDDSDEs, in short). The main aim of this paper is to establish the stability for TDDSDEs. Sufficient conditions are provided to guarantee the solutions to be stable in different senses with regard to a part of the variables in terms of a Lyapunov function. Two examples are given to show the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a novel stable economic model predictive control (EMPC) strategy for constrained nonlinear systems with changing economic criteria. The traditional EMPC may lead to infeasibility and even instability of the closed-loop system when the criterion has been changed. Firstly, a generalised terminal constraint is introduced to ensure the recursive feasibility of the economic optimisation problem, which enforces the terminal states to converge to an arbitrary equilibrium state rather than a predetermined fixed one at the initial time. Then the stability constraint is constructed by solving an auxiliary optimisation problem online, which is the key to guaranteeing the asymptotic stability of the closed-loop system. Finally, sufficient conditions for feasibility and asymptotic stability are derived in the context of changing economic criteria. The main feature of the proposed strategy is that it does not need to know the changes of economic criterion in advance, and its properties and effectiveness are exemplified by simulations on a nonlinear chemical process example. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples. [ABSTRACT FROM AUTHOR]

This paper deals with the integration of input move-blocking into the framework of suboptimal model predictive control. The blocked input parameterisation is explicitly considered as a source of suboptimality. A straightforward integration approach is to hold back a manually generated stabilising fallback solution in some buffer for the case that the optimiser does not find a better input move-blocked solution. An extended approach superimposes the manually generated stabilising warm-start by the move-blocked control sequence and enables a stepwise improvement of the control performance. In addition, this contribution provides a detailed review of the literature on input move-blocked model predictive control and combines important results with the findings of suboptimal model predictive control. A numerical example supports the theoretical results and shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the existence and uniqueness of almost automorphic solutions in distribution to McKean–Vlasov stochastic differential equations are established provided the coeffcients satisfy some suitable conditions. The asymptotic stability of the unique almost automorphic distribution solution is discussed in the square-mean sense. Finally, some examples are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, an uncertain nonlinear switched system is actually a nonlinear switched system disturbed by subjective uncertainties, usually written as several uncertain differential equations. Stability analysis of switched systems has been discussed in depth, while few results about stability of uncertain switched systems were published before. To fill this gap, stability in measure and asymptotic stability of uncertain nonlinear switched systems with countable switches in infinite-time horizon are both considered. The essential property of the solutions to such uncertain switched systems will be illustrated and captured from different perspectives with the help of the above stability analysis. Two theorems to judge these stabilities are proposed and then verified according to uncertainty theory and Lyapunov's second method. At last, a practical model of population growth is studied to display the validness of the results derived. [ABSTRACT FROM AUTHOR]

In this paper, the problem of stability condition for mixed delayed stochastic neural networks with neutral delay and leakage delay is investigated. A novel Lyapunov functional is constructed with double and triple integral terms. New sufficient conditions are derived to guarantee the global asymptotic stability of the concerned neural network. This paper is more general than the paper by Zhu et al. [Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process. Lett. 41 (2015), pp. 1-27]. In our paper, we considered both the neutral delay and leakage delay, but the paper by Zhu et al. is not considering the neutral delay. Also we employed triple integrals in the Lyapunov functional which is not used in the paper by Zhu et al. Finally, two numerical examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two's complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters. [ABSTRACT FROM AUTHOR]

This paper studies a fully parabolic chemotaxis system with competitive kinetics and fractional diffusion of order α 1 , α 2 ∈ (0 , 2) { u t = − d 1 Λ α 1 u − χ 1 ∇ ⋅ (u ∇ w) + μ 1 u (1 − u − a 1 v) , x ∈ T 2 , t > 0 , v t = − d 2 Λ α 2 v − χ 2 ∇ ⋅ (v ∇ w) + μ 2 v (1 − v − a 2 u) , x ∈ T 2 , t > 0 , w t = d 3 Δ w − γ 1 w + γ 2 u + γ 3 v , x ∈ T 2 , on two dimensional periodic torus T 2 . It is proved that (1) has a unique global bounded solution for all appropriately regular nonnegative initial data u 0 , v 0 and w 0 . Moreover, if μ 1 and μ 2 ( μ 1 or μ 2 ) are large enough, we can reach the following conclusions by constructing appropriate energy functional: (i) 0 < a 1 , a 2 < 1 (u , v , w) (⋅ , t) → (1 − a 1 1 − a 1 a 2 , 1 − a 2 1 − a 1 a 2 , γ 2 (1 − a 1) + γ 2 (1 − a 2) γ 1 (1 − a 1 a 2)) uniformly in T 2 as t → ∞. (ii) a 1 ≥ 1 , 0 < a 2 < 1 (u , v , w) (⋅ , t) → (0 , 1 , γ 3 γ 1 ) uniformly in T 2 as t → ∞. (iii) 0 < a 1 < 1 , a 2 ≥ 1 (u , v , w) (⋅ , t) → (1 , 0 , γ 2 γ 1 ) uniformly in T 2 as t → ∞. [ABSTRACT FROM AUTHOR]

There is a great demand for vision-based robotics solutions that can operate using Global Positioning Systems (GPS), but are also robust against GPS signal loss and gyroscope failure. This paper investigates the estimation and tracking control in application to a Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicle (UAV) in six degrees of freedom (6 DoF). A full state observer for the estimation of VTOL-UAV motion parameters (attitude, angular velocity, position, and linear velocity) is proposed on the Lie Group of S E 2 (3) × R 3 = S O (3) × R 9 with almost globally exponentially stable closed-loop error signals. Thereafter, a full state observer-based controller for the VTOL-UAV motion parameters is proposed on the Lie Group with a guaranteed almost global exponential stability. The proposed approach produces good results without the need for angular and linear velocity measurements (without a gyroscope and GPS signals) utilising only a set of known landmarks obtained by a vision-aided unit (monocular or stereo camera). The equivalent quaternion representation on S 3 × R 9 is provided in the Appendix. The observer-based controller is presented in a continuous form while its discrete version is tested using a VTOL-UAV simulation that incorporates large initial error and uncertain measurements. The proposed observer is additionally tested experimentally on a real-world UAV flight dataset. [ABSTRACT FROM AUTHOR]

We consider an abstract model of two coupled elastic materials. One of the materials has conservative characteristics, whereas the other one has dissipative properties. The dissipative effect is caused by the presence of a memory term that depends on the fractional stationary operator with exponent θ ∈ [ 0 , 1 ]. In this paper, we study the asymptotic behavior of the solutions for this system. We show that the solutions decay polynomially with the rate t − 1 / (4 − 2 θ) . For problems with that level of generality, we show that the above rate is the best. We also study the asymptotic behavior when the wave propagation speeds of both materials coincide. For this case, we find that the decay rate is so fast as t − 1 / (2 − 2 θ) for θ ≠ 1. For completeness, we also approach the case θ = 1 , where an exponential decay of solutions is obtained. [ABSTRACT FROM AUTHOR]

In this paper, a novel state-dependent switching controller with delayed positive partial state feedback is proposed to stabilise a controlled system with insufficient state information. At first, the controlled system is converted to a single-degree-of-freedom vibrational system by using an invertible transform and a second-order Taylor approximation for the time delay term. Then, appropriate control gain parameters and a state-dependent switching rule are designed via the physical meaning of the resulting vibrational system. By combining the advantages of delayed positive position feedback with the state-dependent switching mechanism, we find that the time delay can considerably improve the asymptotic stability of the controlled system. Finally, three numerical examples show that the proposed controller is effective and that time delay indeed plays a prominent positive role in switched control systems. [ABSTRACT FROM AUTHOR]

This paper investigates the stability for a class of distributed-order nonlinear systems via event-triggered control method. First of all, an inequality of the solution is established for distributed-order nonlinear inequality systems by employing Laplace transform. And then, by designing an appropriate state feedback controller and event-triggered strategy, and using Lyapunov stability theory and matrix inequality technique, a sufficient condition to ensure the asymptotic stability of the considered distributed-order nonlinear systems is obtained in the form of linear matrix inequality. Moreover, a criterion to exclude Zeno behaviour in event-triggered strategy is provided. Finally, the feasibility and effectiveness of the proposed method are verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we investigate three concepts of stability for linear two-dimensional systems: the 'good' structural stability (an algebraic property linked to the location of the roots of a certain characteristic polynomial), the 'bad' asymptotic stability (roughly the trajectory converges to the equilibrium point) and the 'ugly' exponential stability (the rate of convergence is at least exponential). More precisely, we show that for a usual set of boundary conditions taken along the positive semi-axes, structural stability and exponential stability are equivalent notions. For this particular set of boundary conditions, we further prove that structural stability implies asymptotic stability but a counterexample shows that asymptotic stability does not imply structural stability which is a major difference compared to the one-dimensional case. This also highlights the importance of the boundary conditions when one works with multidimensional systems. [ABSTRACT FROM AUTHOR]

The problems of unconstrained optimisation and establishing asymptotic stability have much in common. Understanding the analogy between these two sheds light on their interconnection and may lead to a number of new results. For instance, in this paper, we provide estimates of the rate of convergence when analysing asymptotic stability of differential equations, rather than just ascertain the very fact of stability. Also, standard methods for the design of Lyapunov functions (e.g. those having the meaning of the full energy of the system) turn out to be unsatisfactory from this point of view and have to be modified. These claims are exemplified in the paper by considering the heavy-ball method for function minimisation ‘in parallel’ with the problem of asymptotic stability for the synchronous motor equation. [ABSTRACT FROM AUTHOR]

In many smart systems, such as cloud computing, networked control, manufacturing, and telecommunication, the effects of time delays are unavoidable. Saturation nonlinearity is common in many smart systems (e.g. electric systems with limited actuator power supplies, mechanical systems with position and speed constraints, fixed-point digital filters, etc.). Therefore, the study of stability of discrete-time systems (DTSs) with time delay and saturation is of high importance in practice. The global asymptotic stability (GAS) problem of such systems is investigated in this paper. The saturation nonlinearity is constrained by a convex hull with a free matrix whose infinity norm is smaller than or equal to unity. A new Lyapunov-based GAS criterion for DTSs with time-varying delay and state saturation is established. The GAS problem for DTSs with constant delay and saturation is also discussed. The obtained results can be used to ensure the absence of overflow oscillations in the considered system. In comparison to several existing criteria, the approach yields improved stability results. An example is provided to demonstrate the importance of the presented results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the practical stability in relation to a part of the variables of stochastic pantograph differential equations (SPDEs, in short). With the aid of Lyapunov function method, the criterions of the global practical uniform asymptotic stability and the global practical uniform p-th moment exponential stability in relation to a part of variables of SPDEs are established. An illustrative example is given to show the effectiveness and feasibility of the proposed results on the practical stability with respect to a part of variables. [ABSTRACT FROM AUTHOR]

This paper addresses the invariant [ K , K L ] sector as a special class of [ K , K L ] sector that holds the invariant characteristics with some appropriate control input, i.e. the energy of the system drastically decreases and state trajectory always remains inside the sector once it moves into it by the suitable control signal. The analysis of the nonlinear sector is regarded in comparison function prospective to outreach the property of uniformity. Here, the construction of [ K , K L ] sector and invariant [ K , K L ] sector relies on the selection of well-suited control-Lyapunov function. The switching control with invariant [ K , K L ] sector is designed to ensure the state trajectories move inside the nonlinear sector in finite-time and stay inside for all future time. Finally, the effectiveness of the proposed algorithm is illustrated with real physical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the long-time behaviour of the numerical solutions to a class of linear non-autonomous neutral delay differential equation with proportional delays. Our purpose is to give some asymptotic estimates of theθ-methods with constant stepsize discretization and formulate their upper bounds. Asymptotic estimate not only describes more accurate than asymptotic stability, but also gives an upper bound estimate of the solution for the long-time behaviour. We also compare the known results and show that our formulae improve and generalize these results. Some numerical examples are given in the end of this paper to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of Poisson Stepanov-like almost automorphy (or PoissonS2-almost automorphy). Under some suitable conditions on the coefficients, we establish the existence and uniqueness of Stepanov-like almost automorphic mild solution to a class of semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solution. Finally, we give an example to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the asymptotic stability of the Riemann–Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear discrete-time dynamical systems. The solution is based on the concept of the-functions introduced in this paper. As a result, new necessary and sufficient conditions for asymptotic stability of such systems and an estimation or the exact determination of the asymptotic stability domain of the stateare established. Examples are worked out to illustrate the results. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a porous thermoelastic system where the heat conduction is given by Coleman–Gurtin's law. We show that the system is exponentially or polynomially stable depending on a relationship between the coefficients of wave propagation speed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate stabilisation of hybrid stochastic systems with time-varying delay by feedback control based on discrete-time state and mode observations with a time delay. By constructing a proper Lyapunov functional, the H ∞ , asymptotic and exponential stability of the controlled systems are studied in the pth moment sense for p>1. Meanwhile, we obtain the upper bound on the duration τ between two consecutive state and mode observations. At last, two numerical examples are illustrated to support our theoretical results. [ABSTRACT FROM AUTHOR]

The main concern of this paper is to investigate the asymptotic stability of stationary solution to the compressible Navier–Stokes–Poisson equations with the classical Boltzmann relation in a half line. We first show the unique existence of stationary solution with the aid of the stable manifold theory, and then prove that the stationary solution is time asymptotically stable under the small initial perturbation by the elementary energy method. Finally, we discuss the convergence rate of the time-dependent solution towards the stationary solution, and give a new condition to ensure an algebraic decay or an exponential decay. The proof is based on a time and space weighted energy method by fully utilizing the self-consistent Poisson equation. [ABSTRACT FROM AUTHOR]

This paper deals with the initial-boundary value problem for the two-species chemotaxis-competition system with two signals ∂ t u 1 = Δ u 1 − χ 11 ∇ ⋅ (u 1 ∇ v 1) − χ 12 ∇ ⋅ (u 1 ∇ v 2) + μ 1 u 1 (1 − u 1 − a 1 u 2) , ∂ t u 2 = Δ u 2 − χ 21 ∇ ⋅ (u 2 ∇ v 1) − χ 22 ∇ ⋅ (u 2 ∇ v 2) + μ 2 u 2 (1 − u 2 − a 2 u 1) , 0 = Δ v 1 − λ 1 v 1 + α 11 u 1 + α 12 u 2 , 0 = Δ v 2 − λ 2 v 2 + α 21 u 1 + α 22 u 2 , under the homogeneous Neumann boundary condition, where x ∈ Ω , t > 0 , χ i j > 0 , μ i > 0 , a i > 0 , α i j > 0 , λ i > 0 (i , j = 1 , 2) , and Ω ⊂ R n (n ≥ 2) is a smooth bounded domain. If χ 11 / μ 1 , χ 12 / μ 1 , χ 21 / μ 2 and χ 22 / μ 2 are sufficiently small, then the system possesses a globally bounded classical solution for any suitably regular initial data u 10 , u 20 . Furthermore, by constructing some appropriate functionals, it is shown that For the weak competition case, if μ 1 , μ 2 are sufficiently large, then the solution (u 1 , u 2 , v 1 , v 2) converges to 1 − a 1 1 − a 1 a 2 , 1 − a 2 1 − a 1 a 2 , α 11 (1 − a 1) + α 12 (1 − a 2) λ 1 (1 − a 1 a 2) , α 21 (1 − a 1) + α 22 (1 − a 2) λ 2 (1 − a 1 a 2) exponentially as t → ∞. For the strong-weak competition case, if μ 2 is sufficiently large, then the solution (u 1 , u 2 , v 1 , v 2) converges to (0 , 1 , α 12 / λ 1 , α 22 / λ 2) with exponential decay when a 1 > 1 , and with algebraic decay when a 1 = 1. [ABSTRACT FROM AUTHOR]

This paper is devoted to deal with the stabilisation problems of continuous-time hybrid stochastic systems (often described by stochastic differential equations with Markovian switching) with Lévy noise by feedback controls based on discrete-time state observations. There are so far few results on the stabilisation of continuous-time hybrid stochastic systems with Lévy noise based on discrete-time state observations, despite the stabilisation of stochastic systems by discrete-time feedback controls has been investigated in general. Precisely, it is discussed the stabilisation in the sense of H ∞ -stability, asymptotic stability, mean-square exponential stability and almost sure exponential stability for such systems. It is also presented an upper bound on the duration τ between two consecutive state observations by means of the Lyapunov function. Two examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

Meshfree method based on radial basis functions is a popular tool used to numerically solve partial differential equations. This paper deals with the convergence and stability of the proposed method for hyperbolic partial differential equations with piecewise constant arguments. Firstly, we apply central difference to the time variable and θ-weighted finite difference to the original equation simultaneously, then the numerical scheme is obtained by using the meshfree method based on radial basis functions to approximate the unknown function and its second-order spatial derivative. Secondly, the convergence is analysed in L ∞ -norm and the sufficient conditions for asymptotic stability of the numerical solution are acquired under which the analytic solution is asymptotically stable. Finally, our study is supported by several numerical experiments. [ABSTRACT FROM AUTHOR]

In this digital era, the basis of every smart instrument is discrete signal models e.g. in Networked control systems, Cyber physical systems etc. It has been shown that time-delays are unavoidable during the digital implementation of an engineering system. Therefore, the stabilization of discrete time delayed systems is gaining the high importance [1–10]. Although a lot of literature is found on the stabilization of time delayed systems for a long time using the construction of proper non-negative Lyapunov functional. Recalling some existing results on this issue, the LMI-based stability conditions are obtained by its forward difference negative-definite in direction to claim the less conservative results [15–25]. In order to seek less conservative stability criteria, this paper introduces an anti-windup scheme appended with Wirtinger inequality, reciprocal convex approach and delay partitioning of a discrete-time delayed systems by using Lyapunov Krasovskii functional. To accomplish this task, delay partitioning technique may be utilized to develop improved stability conditions for the considered system. The Wirtinger-based inequality and reciprocal convex approach has been employed to derive less conservative results. On employing the delay partitioning, a novel linear matrix inequality-based criterion is proposed to stabilize such systems. The considered Lyapunov-Krasovskii functional includes the information of intermediate delay to acknowledge the delay information implicitly that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. The estimation of the attraction basin is to ensure that the state remains inside the level set of a certain Lyapunov function. Numerical simulation verifies that the presented method reduces conservatism than the existing results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive robust boundary controller is designed for an unstable heat equation with external disturbance flowing into the control end. The disturbance and uncertainty effect is cancelled out in the closed-loop system by using on-line approximation of disturbance upper-bound provided as an output of adaptive robust update law. The asymptotic stability of the controlled system in the presence of unknown disturbance and/or parametric uncertainties is proved utilising the Lyapunov theorem. Unlike previous researches, the control implementation does not require prior knowledge of unknown disturbance. Moreover, the controller does not require measuring the system states or estimating the system states by an observer. The adaptive robust controller can be regarded as a combination of the best qualities of the adaptive controller and the robust controller with no prior knowledge of system uncertainty, and asymptotic tracking error performance. Numerical simulations and comparisons are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in. The approach being used allows the vector field to be discontinuous on the switching plane. It is shown that the discontinuity of the vector field plays a crucial role in global asymptotic stability. This point is illustrated by examples, where the change in the discontinuity of the vector field (without changing the eigenvalues of subsystems) can cause the system to be globally asymptotically stable or unstable. [ABSTRACT FROM PUBLISHER]

In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper discusses grasping and orientation control of an object by dual one-link Timoshenko arms. The control objective is to control the grasping force and the orientation of the object, and to suppress the vibration of the arms at the same time. For this objective, we derive a boundary controller based on the total energy of the system described by a hybrid PDE-ODE model, and asymptotic stability of the closed-loop system is proven by the LaSalle's invariance principle. In addition, numerical simulations are conducted and the results indicate that the derived controller can realise the grasping and orientation control of an object by dual one-link Timoshenko arms. [ABSTRACT FROM AUTHOR]

In this paper, we develop a population equation based on the Ricker model with periodic carrying capacity and embedded mechanisms of both weak and strong types of Allee effect: x (n + 1) = x (n) exp ⁡ (r (1 − x (n) K (n) ) (1 − A + C x (n) + C)) , n ∈ N 0. We prove a persistence property and existence of periodic solutions in each case of Allee effect. We find sufficient conditions for the periodic solution to be globally asymptotically stable and sufficient conditions for this solution to become unstable. We show that the mechanism of weak Allee effect increases the range of stability for the periodic solution. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization problem of one-dimensional Schrödinger equation with boundary disturbance is concerned. The variable structure control technique is adopted to design the nonlinear feedback controller. For the Schrödinger system, the observation blind point problem is discussed and the relationship between the initial data and observation blind point is given. According to a theorem which can be regarded as an extended version of the Lions–Lax–Milgram theorem, the existence and uniqueness of the solution for the system are proved. Finally, a sufficient condition for the asymptotic stability of the system is provided. As a remark, the asymptotic stability, which can be realized by the control, is also presented. [ABSTRACT FROM AUTHOR]

In this paper, a family of equations with uncertain values of parameters is investigated. An application of mixed Minkovski volumes is proposed, and conditions for stability, asymptotic stability and instability of the stationary solutions are established. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a stochastic susceptible-infective-removed-infective (SIRI) epidemic model with relapse. We show that the densities of the distributions of the solutions can converge in L 1 to an invariant density or can converge weakly to a singular measure under certain condition. We also find the support of the invariant density. Moreover, we establish sharp sufficient criteria for the extinction of the disease in two cases. The results show that the smaller white noise can assure the existence of a stationary distribution which implies the persistence of the disease while the larger white noise can lead to the extinction of the disease. [ABSTRACT FROM AUTHOR]

In this paper, we consider a viscoelastic plate equation with a velocity-dependent material density and a logarithmic nonlinearity. Using the Faedo-Galaerkin approximations and the multiplier method, we establish the existence of the solutions of the problem and we prove an explicit and general decay rate result. These results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

Ordinary differential equations (ODEs) have a wide range of potential applications in science and engineering with regard to nonlinear dynamic systems. Frequently, there is a focus upon locating unique solutions to ODEs, with non-unique solutions being viewed as potentially problematic. However, some have recognized the importance of examining the character of non-unique solutions as well in order to properly understand the behaviour of physical systems. In some areas of engineering, notably control theory, the latter concern has become pressing. In this paper, by studying the asymptotic stability of second-order ordinary differential systems, we present a theorem creatively and prove it strictly by two lemmas. Using the criteria for non-unique solutions of first-order ordinary differential equations at points of equilibrium, we can solve engineering problems effectively. The applicability of this novel approach to the solution of engineering problems is provided through an example relating to the optimization of finite time controllers. [ABSTRACT FROM AUTHOR]

In this paper, a robust adaptive tracking controller is proposed for a nonholonomic wheeled mobile robot (WMR) in the presence of unknown wheel slips. The role of the Gaussian wavelet network in this proposed controller is to approximate unknown smooth nonlinear dynamic functions due to no prior knowledge of the dynamic parameters of the WMR. In addition, one robust law is employed at the kinematic level so as to compensate the harmful effects of the unknown wheel slips, and another robust law is used at the dynamic level to overcome total uncertainties caused by dynamic parameter variations, external disturbances, etc. The stability of the whole closed-loop control system is proved in accordance with Lyapunov theory and Barbalat's lemma. Ultimately, the simulation results are shown in comparison with those of another control method under the same condition to confirm the validity and efficiency of this proposed control method. [ABSTRACT FROM AUTHOR]

We address the stability of stationary solutions to a class of 2D non-newtonian fluid equations, when the external force contains hereditary characteristics involving unbounded delays. Firstly, when the unbounded variable delay is driven by a continuously differential function, we establish the stability of nontrivial weak stationary solutions and the asymptotic stability of trivial stationary solution. Then when the general unbounded delay is continuous with respect to time, the stability of nontrivial strong stationary solutions is also obtained. Eventually, when the proportional delay is considered, the polynomial stability of trivial stationary solution is verified. [ABSTRACT FROM AUTHOR]

The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, the trajectory tracking problem of a proton exchange membrane (PEM) fuel cell is considered. To solve this problem, stable and optimal controllers are proposed. The stable and optimal techniques have the objective that the system states should reach the desired trajectories while in the first, the tracking error is minimised, and in the second, the tracking error and inputs are minimised. The effectiveness of the proposed techniques is verified by simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior for a one-dimensional non-autonomous full von Kármán beam with a thermo-viscoelastic damping in the internal feedback. By introducing a suitable energy and some Lyapunov functionals, under some restrictions on the non-autonomous functions and the relaxation function, we show the asymptotic behavior of the solution and establish a general decay result for the energy. [ABSTRACT FROM PUBLISHER]

In this paper, the Galerkin finite element method is applied to solve the generalized delay reaction-diffusion equation, where the spatial and temporal variables are discretized by the Galerkin finite method and the Crank–Nicolson method, respectively. The numerical treatment shows that the proposed numerical scheme is asymptotically stable. Moreover, some a priori estimates of L 2 and L ∞ -norms and with optimal order of convergence C (h 2 + (Δ t) 2 )) are obtained. The numerical experiments illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Since Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) byfeedback controls based on discrete-time state observationsin 2013, many authors have further studied and developed it. However, so far no work on thepth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense ofH∞, asymptotic and exponential stability inpth moment for allp> 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities. [ABSTRACT FROM AUTHOR]

In this paper, a class of sampled-data systems with double feedbacks are scrutinized for internal/external stability through the open-/closed-loop characteristic polynomials contraposition. A sampled-data system with double feedbacks consists of a continuous-time plant and two feedback control loops: a discrete-time one for digital control objectives with sampler and zero-order hold synchronized, and a continuous-time one for analog control performances. Contraposition stability criteria are worked out by exploiting what we call the contraposition return difference relationship in between the open- and closed-loop characteristic polynomials defined via the lifted model. The criteria for asymptotical stability are necessary and sufficient, independent of open-loop poles distribution of the lifted model and locus orientation specification. Moreover, the criteria forLp-stability are sufficient, while retaining the technical merits of the criteria for asymptotical stability. All criteria present stability conditions in the standard discrete-time sense that are implementable either graphically with loci plotting, or numerically without loci plotting. Examples are included to illustrate the results. [ABSTRACT FROM PUBLISHER]