Problem Of Exponential Stability Research Articles

New Stability Criterion for Positive Impulsive Fuzzy Systems by Applying Polynomial Impulse-Time-Dependent Method.

The problems of exponential stability and L1 -gain for positive impulsive Takagi-Sugeno (T-S) fuzzy systems are further studied in this article. Different from the Lyapunov function in the literature, where the Lyapunov matrices are time-invariant or only linearly dependent on the impulse interval, in this article, a novel polynomial impulse-dependent (ID) copositive Lyapunov function (CLF) is constructed by using the polynomial impulse time function. In addition, the binomial coefficients are applied to derive new finite linear programming conditions. Less conservative results are obtained since the polynomial ID CLF contains more impulse interval information. Three examples demonstrate the influence of the polynomial degree on the results and the effectiveness of the developed new results.

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

ASYMMETRIC FUNCTIONAL-BASED APPROACHTO EXPONENTIAL STABILITY OF LINEAR DISTRIBUTEDTIME-DELAY SYSTEMS

In this paper, the problem of exponential stability of linear time-delay systems with mixed discrete and distributed delays is studied. Based on an asymmetric Lyapunov-Krasovskii functional approach, sufficient conditions are derived in terms of linear matrix inequalities to guarantee the exponential convergence of the system state trajectories with a prescribed decay rate. The efficacy of the obtained results is demonstrated by a given numerical example and simulations.

Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses

This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

Stabilization of impulsive hybrid stochastic differential equations with Lévy noise by feedback control based on discrete-time state observations

In this paper, we investigate the problem of the mean-square exponential stabilization for a class of unstable impulsive hybrid stochastic differential equations with Lévy noise (IHSDEs-LN) via feedback control based on discrete-time state observations. Our results show that if feedback control of continuous-time observations can stabilize the controlled system in the sense of mean-square exponential stability, then feedback control of discrete-time state observations can also stabilize the controlled system. And there exists an upper bound on the interval between adjacent observation moments that can be accurately computed. Based on this new theory, we first design continuous-time feedback control for unstable IHSDEs-LN to achieve the stabilization problem, and then improve the continuous-time feedback control to discrete-time state observations feedback control.

Passivity-Based Stabilization for Switched Stochastic Nonlinear Systems

This paper addresses the passivity-based mean square exponential stabilization problem for switched stochastic nonlinear systems. A concept of generalized small-time normobservability is presented and an appropriate test condition is also provided. For pre-given passivity rate and average dwell time, a set of feedback controllers is designed by use of the passivity property. Then, combining with generalized small-time norm-observability, a sufficient condition to guarantee mean square exponential stabilization of a switched stochastic nonlinear system is given. As a special case, the switched stochastic linear system is also discussed. Finally, a numeral example shows the effectiveness of the proposed method.

Exponential stabilization of the class of the switched systems with mixed time varying delays in state and control

This paper presents the problem of exponential stabilization of switched systems with mixed time-varying delays in state and control. Based on the partitioning of the stability state regions into convex cones, a constructive geometric design for switching laws is put forward. By using an improved Lyapunov–Krasovskii functional in combination with matrix knowledge, we design a state feedback controller that guarantees the closed-loop system to be exponentially stable. The obtained conditions are given in terms of linear matrix inequalities (LMIs), which can be effectively decoded in polynomial time by various computational tools such as the LMI tool in MATLAB software. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Semi-global exponential stabilization of stochastic nonlinear systems with distributed delay under discrete-time state observations and application to circuit systems

This paper is aimed at studying the semi-global exponential stabilization problem for stochastic nonlinear systems with distributed delay under discrete-time state observations. An extended definition of horizontal translation of the segment function along the investigated systems is given, related to the stochastic disturbance and Brownian motion. Basically, the right and upper Dini’s derivative of the constructed functional is presented. Combining this with the global exponential stability of the stochastic nonlinear systems with distributed delay under continuous-time feedback control, the Lyapunov method and Halanay inequality, the maximum observation interval and some stabilization criteria to make the investigated systems under discrete-time state observations reach semi-global exponential stabilization are provided. The results indicate that the semi-global exponential stabilization is dependent upon stochastic disturbance, initial condition range, and maximum observation interval. Finally, an application to the circuit systems is discussed and the involved sufficient conditions for the circuit systems to keep semi-global stabilization are also proposed. Besides, the numerical simulation results confirm the effectiveness of the theoretical results.

Dynamic Event-Triggered Control for Delayed Nonlinear Markov Jump Systems under Randomly Occurring DoS Attack and Packet Loss

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attacks and packet loss. Firstly, the stochastic characteristics of DoS attacks and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of the systems. Then, by constructing a general common Lyapunov functional and combining it with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through two examples.

Mean square exponential stability with l2−l∞ gain of discrete-time switched-Markovian jump systems

In this paper, the problem of mean square exponential stability with [Formula: see text] gain is studied for the discrete-time switched-Markovian jump systems, which are composed of a deterministic switched system and a Markovian jump system. The mode-dependent average dwell time method is adopted to design the switching signal for the deterministic switched system, and the Markovian jump property is presented by the Markov chain, which is dependent on the designed mode-dependent average dwell time switching signal. The multiple discontinuous Lyapunov function is constructed to guarantee the mean square exponential stability and [Formula: see text] performance. Furthermore, a novel inequality is established to show the relationship between multiple discontinuous Lyapunov functions and disturbances to derive the [Formula: see text] performance. Finally, two numerical examples and a circuit system are given to demonstrate the effectiveness of the obtained results.

Data-driven control of singularly perturbed hybrid systems with multi-rate sampling

This paper addresses the exponential stability problem of singularly perturbed hybrid systems with multi-rate sampling. Firstly, a hybrid model is established to describe a class of nonlinear singularly perturbed systems by designing a data-driven mechanism and multi-rate sampling controller. Secondly, a novel error function and several inequalities are proposed to obtain the properties of the error subsystems. Thirdly, we estimate the bounds of fast and slow sampling intervals, and analyze the effect of the perturbation parameter and fast-slow sampling ratio on the sampling intervals. Finally, a DC motor model is illustrated to demonstrate the effectiveness of the proposed results.

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.

Adaptive Control With Global Exponential Stability for Parameter-Varying Nonlinear Systems Under Unknown Control Gains.

It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this article, without the need for PE condition, we address the problem of global exponential stabilization of strict-feedback systems with mismatched uncertainties and unknown yet time-varying control gains. The resultant control, embedded with time-varying feedback gains, is capable of ensuring global exponential stability of parametric-strict-feedback systems in the absence of persistence of excitation. By using the enhanced Nussbaum function, the previous results are extended to more general nonlinear systems where the sign and magnitude of the time-varying control gain are unknown. In particular, the argument of the Nussbaum function is guaranteed to be always positive with the aid of nonlinear damping design, which is critical to perform a straightforward technical analysis of the boundedness of the Nussbaum function. Finally, the global exponential stability of parameter-varying strict-feedback systems, the boundedness of the control input and the update rate, and the asymptotic constancy of the parameter estimate are established. Numerical simulations are carried out to verify the effectiveness and benefits of the proposed methods.

Novel Criteria for Exponential Stability of Neutral Functional Differential Equations

We address the challenging problem of exponential stability of general neutral functional differential equations. By a novel approach, we present some new explicit criteria for the exponential stability of neutral functional differential equations. Some remarks and illustrative examples are given.

Dynamic learning from adaptive neural control for full-state constrained strict-feedback nonlinear systems

This study focuses on the learning and control issues of strict-feedback systems with full-state constraints. To achieve learning capability under constraints, transformation mapping is utilized to convert the original system with full-state constraints into a quasi-pure-feedback unconstrained system. Utilizing the system transformation technique, only a single neural network (NN) is required to identify the unknown dynamics within the transformed system. Combining the dynamic surface control design, a novel adaptive neural control scheme is developed to ensure that all closed-loop signals are uniformly bounded, and every system state remains within the predefined constraint range. In addition, the precise convergence of NN weights is further transformed into an exponential stability problem for a category of linear time-varying systems under persistent excitation conditions. Subsequently, the converged NN weights are efficiently stored and utilized to create a learning controller to achieve better control performance while abiding by the full-state constraints. The viability of this control strategy is demonstrated via simulations.

Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays

This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.

Global exponential stability and stabilization of stochastic memristive neural networks with spatial diffusions and hybrid delays

In this paper, the global exponential stability and stabilization problems are investigated for memristive neural networks (MNNs) with stochastic disturbances, spatial diffusions and distributed delays. The spatial diffusions are not assumed to be symmetric and distributed delays are relaxed to be unbounded. Then, the presented MNNs are modeled as a class of stochastic partial systems with hybrid delays. Based on nonsmooth analysis, the Lyapunov–Krasovskii functional and inequality approach, some simple algebraic criteria are derived for the global exponential stability as well as the stabilization via two kinds of designed feedback controllers. The derived criteria are easily verified and the obtained results are available for other delayed systems with or without stochastic disturbances and spatial diffusions. Finally, the stability and stabilization results are validated by numerical simulations.

Adaptive event-triggered control for stability of fractional-order T-S fuzzy multi-links complex networks with random coupling delay

The main concern of this article is to address the exponential stability problem of fractional-order T-S fuzzy multi-links complex networks through designing the novel intermittent adaptive event-triggered control (IAE-TC) scheme. To reduce unnecessary transmission burden as much as possible in an allowable range, dynamic variable is introduced into fuzzy intermittent adaptive control and then fuzzy intermittent adaptive event-triggered control is established. In this control scheme, the controller is only activated when the event triggering conditions are not met, and has adaptability to the evolution results of the controlled network. Furthermore, by applying the Lyapunov method, the graph theory and the IAE-TC strategy, exponential stability criteria of the proposed networks are deduced. Meanwhile, we prove that Zeno behavior does not exist. Ultimately, an application about fractional-order T-S fuzzy multi-links competitive neural networks model is given to demonstrate the validity of the results, simultaneously, we show some numerical simulations.

On exponential stability in [formula omitted]th moment of neutral Markov switched stochastic time-delay systems

In this article, the problem of the pth moment exponential stability is be investigated for neutral Markov switched stochastic time-delay systems. By virtue of inequalities based on the state-dependent multiple Lyapunov functions, we propose adequate conditions for the p-ES of Markov switched neutral stochastic differential delay equation applying properties for the stationary distribution of Markov switched process. For a class of neutral Markov switched stochastic time delay systems with impulse, several new criteria for pth moment exponential stability is obtained using the impulse average dwell-time condition, the integral transformation inequality, and stochastic analysis theory. The results extend and improve the related results from the existing literature. Some examples are provided to illustrate the validity of our derived results.