Sufficient Conditions For Stability Research Articles

Stabilization with unknown-input estimation for time-delayed systems using functional-observer-based feedback control design

This paper focuses on the stabilization and unknown-input estimation (UIE) problem of continuous-time delayed systems by virtue of functional-observer (FO)-based feedback controller. It allows us to estimate the unknown external variable that degrades the system performance with respect to the partially known input of the system. In particular, the unknown inputs are considered in system dynamics’s state as well as in output, which makes the addressed problem to be more applicable. In addition to that, the aim is then to design minimal order functional observer. Notably, the FO-based feedback control law is introduced for the first time and it is used to ensure the asymptotic stabilization with UIE of the proposed system. Whilst, the design and analysis of UIE and FO is based on Lyapunov stability theory and applying the inequality analysis technique, the sufficient stability conditions are established in the forms of matrix inequality. Eventually, the numerical examples with simulation results are provided to validate the practicability and efficacy of the developed control strategy.

Stability and Bifurcation Control for a Generalized Delayed Fractional Food Chain Model

In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system’s Hopf bifurcation. The results indicate that adjusting the control intensity or the control target’s age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems.

On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas

   The one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and variable in a continuum of velocities. The absolute instability of all considered one-dimensional dynamic states of any local thermodynamic equilibrium was proved using the direct Lyapunov method. The scope of applicability of the Newcomb–Gardner–Rosenbluth sufficient condition for linear stability was outlined. An a priori exponential estimation was obtained for the rise of small one-dimensional perturbations from below. Analytic counterexamples to the spectral Newсomb–Gardner theorem and the Penrose criterion were constructed. Earnshaw’s theorem was extended from classical mechanics tostatistical one.

Observer-based control for large-scale interconnected systems with parameter uncertainty and application to wireless power transfer systems

In the work, the observer-based control is designed and analyzed for a class of large-scale interconnected systems subject to parameter uncertainty. In the beginning, we build a large-scale interconnected system with parameter uncertainty and apply this model to a multi-level wireless power transfer system. By using this modeling method, the order of multi-level wireless power transfer system is greatly deduced. In addition, the multi-level wireless power transfer system include coupling terms and uncertain parameters considered in the observer-based control law design. We earn sufficient conditions of this model stability for multi-level wireless power transfer systems under this control law through the Lyapunov stability theorem and Young’s inequality. The stability analysis method suggested in the work could also be adopted in other practical plants. At last, the correctness and availability of this suggested approach are verified through simulation results.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Sufficient Conditions for Uniform Asymptotic Stability and Input-to-State Stability Using High-Order Control Barrier Functions

Sufficient Conditions for Uniform Asymptotic Stability and Input-to-State Stability Using High-Order Control Barrier Functions

Adaptive event-triggering mechanism based Takagi-Sugeno fuzzy automatic generation controller design for offshore wind power system

Interconnected offshore wind power system (OWPS) attracts widespread attention due to its special advantage. With the development of wind power technology, higher requirements are put forward for the reliability of networked OWPS. Considering the nonlinear characteristics of OWPS and limited network bandwidth resource, an adaptive multi-event triggering mechanism based distributed Takagi-Sugeno fuzzy robust H∞ control scheme is investigated in this paper. A modeling method for OWPS integrating communication constraints is proposed. By Lyapunov stability theory, the sufficient condition for the asymptotical stability of OWPS has been derived. Compared with traditional control scheme, the proposed Takagi-Sugeno fuzzy controller provides smoother output power, smaller torque oscillation and higher wind energy utilization. Furthermore, the co-design strategy increases the utilization rate of network bandwidth. The feasibility of adaptive multi-event triggering mechanism based Takagi-Sugeno fuzzy controller is demonstrated through a simulation example.

CBF‐guided iterative learning control performance optimization for switched systems

AbstractThis article studies the control barrier function (CBF) guided tracking performance optimization for switched systems under iterative learning control (ILC). CBF is an effective method for handling control system state safety. If the safe set is designed as expected performance, and the unsafe set is not expected, then this may be a good choice for optimizing control system performance. We propose a tracking performance optimization method based on CBF to speed up the convergence of the tracking error. A safe set is used to describe the expected tracking performance, by utilizing CBF, safety is further transformed into a set of inequality conditions that constrain ILC controller gains, which ensures that the tracking error is always within the safe set. In addition, an event‐triggering mechanism (ETM) is considered to reduce unnecessary data transmission, and sufficient conditions for exponential stability of the tracking error of switched systems and ILC controllers design are obtained. Finally, a simulation example is given to verify the feasibility of the proposed method.

Adaptive event-triggered control for neural network–approximated switched systems under injection attacks

This paper studies the event-triggered control for uncertain switched systems under injection attacks. An adaptive event-triggered control method for neural network–approximated switched systems (NNA-SSs) is proposed. The main works are as follows: First, a neural network is introduced to approximate the uncertain nonlinear item of the systems. Second, the observer-based adaptive event-triggering (OB-AET) strategy is designed to efficiently utilize communication and computing resources. Furthermore, the closed-loop switched systems considering injection attacks are established. By utilizing the Lyapunov function method and average dwell time technique, sufficient conditions for the exponential stability of the closed-loop switched systems are given. Accordingly, the gains of the state feedback controllers and observers are solved. Finally, simulation examples are given to verify the effectiveness of the proposed method.

Sufficient and necessary conditions of exponential stabilisation for a class of distributed second-order semilinear systems with time delay

In this paper, we investigate the problem of exponential stabilisation for a class of retarded distributed second-order semilinear systems by means of a bounded feedback control. The existence and uniqueness of mild solution for the considered systems are proved in Hilbert space framework. Sufficient and necessary conditions for exponential stabilisation are given. Some illustrating applications are provided.

Finite-time stability and stabilisation of time-varying stochastic systems with multiplicative noise and time-delays

This article investigates the problem of finite-time stability and stabilisation (FTSS) in time-varying stochastic systems with multiplicative noise and time-delays. To simplify research process, the method of dimension expansion is employed to transform systems characterised by constant delays into delay-free models, which enables the extraction of the finite-time stability (FTS) of the original systems by leveraging the FTS analysis conducted on the new model. Two distinct approaches are employed to establish criteria for determining FTSS in systems. The first approach leverages the state transition matrix (STM) method to acquire both necessary and sufficient stability conditions for the simplified models. Furthermore, sufficient conditions for the FTS of the original systems can be obtained. For ease of verification, our second approach integrates the Lyapunov equation with linear matrix inequalities (LMIs), offering a framework to obtain control gains. Finally, the proposed results are instantiated through three simulation examples to demonstrate their efficacy.

Convergence and Stability of Coupled Belief-Strategy Learning Dynamics in Continuous Games

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players’ strategies and realized payoffs using Bayes’ rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium. Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged.

New Robust Model for Stability and H∞ Analysis for Interconnected Embedded Systems

This paper presents a novel approach to analyzing the robust stability of interconnected embedded systems. The paper starts by discussing the challenges associated with designing stable and robust embedded systems, particularly in the context of interconnected systems. The proposed approach combines the H∞ control theory with a new model for interconnected embedded systems, which takes into account the effects of communication delays and data losses. The paper provides a detailed mathematical analysis of the new model and presents several theorems and proofs related to its stability. The effectiveness of the proposed approach is demonstrated through several practical examples, including a networked control system and a distributed sensor network. The paper also discusses the limitations of the proposed approach and suggests several directions for future research. The proposed filter design method establishes a sufficient condition for the asymptotic stability of the error system and the satisfaction of a predefined H∞ performance index for time-invariant bounded uncertain parameters. This is achieved through the use of the strict linear matrix inequalities (LMI) approach and projection lemma. The design is formulated in terms of linear matrix inequalities (LMI). Numerical examples are provided to demonstrate the effectiveness of the proposed filter design methods.

Exponential stability and relative controllability of first‐order delayed integro‐differential systems with impulses

We establish sufficient conditions for the exponential stability of nonsingular impulsive delayed integro‐differential systems. Our approach to addressing nonsingular differential problems involves the application of permutable matrices and their associated delayed exponential. Furthermore, we investigate the controllability of a nonlinear impulsive and delayed problem by employing the corresponding Gramian matrix. Finally, to illustrate the theoretical outcomes, we provide examples and graphical representations for each situation.

Stability of Fractional Reaction-Diffusion Memristive Neural Networks Via Event-Based Hybrid Impulsive Controller

This article explores the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms. A novel hybrid impulsive controller triggered by a specific event is proposed to stabilize the network, thereby replacing the conventional approach of modifying network parameters. The proposed controller is proven to prevent Zeno behavior. Sufficient conditions for the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms are established through Lyapunov direct method, inequality techniques, Green’s theorem and impulse analysis. Furthermore, the proposed controller is theoretically shown to be more resource-efficient than the conventional one, and our work extends existing research to make it more suitable for practical application such as pattern recognition, image processing and so on. Finally, an example is provided to illustrate the validity of the findings.

Stability of short memory fractional-order hybrid systems

The stability theory of short memory fractional-order hybrid systems is studied in this article. Sufficient conditions of asymptotic stability and ultimately bounded stability for the nonliear short memory fractional-order hybrid systems are proposed respectively. For the convenience of application, a convenient criterion of stability for the nonliear short memory fractional-order hybrid systems is derived in the study. Demonstrative examples are given to verify the correctness of the proposed theorems in the part of simulation.

Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.

A Decomposition Approach to Multiagent Systems With Bernoulli Packet Loss

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance -- which are expressed in the form of linear matrix inequalities -- scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.

Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

This paper studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the above conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.

Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.