Mean Square Exponential Stability Research Articles

Exponential stability and optimal control of a stochastic brucellosis model with spatial diffusion and nonlocal transmission

In this paper, a stochastic brucellosis model with nonlocal transmission and spatial diffusion is established. Existence, uniqueness and positivity of mild solution to the model are obtained by adopting a truncation method. To ensure the Mean Square Exponential Stability (MSES) of the solution, sufficient conditions are given by employing the inequality techniques and the stability implies that the brucellosis die out in a short period of time. Moreover, we introduce elimination of infected animals and disinfection of brucella to the model as control strategies. Necessary conditions are given to obtain the optimal control which best balance the outcomes and costs of the control by applying Pontryagin’s maximum principle. Finally, the theoretical results are demonstrated by the numerical simulations.

Mean-square exponential stabilization of memristive neural networks: Dealing with replay attacks and communication interruptions

This paper investigates the mean-square exponential stabilization (MSES) of memristive neural networks (MNNs) under replay attacks and communication interruptions. The research will revolve around the following two questions: Firstly, facing replay attacks and communication interruptions, how to design an appropriate controller? Secondly, how to ensure the MSES of MNNs under higher replay attack rate and communication interruption rate? To address these challenges, a novel intermittent sampled-data control scheme is established by considering the mathematical characteristics of replay attacks and communication interruptions. Furthermore, interval-dependent Lyapunov functions are constructed based on the Lyapunov stability theory and inequalities techniques, and two sufficient criteria for MSES of MNNs under the mentioned risks are derived. Thus, the control gain is obtained by solving a series of linear matrix inequalities. In addition, two algorithms are designed to investigate the maximum allowable replay attack rate and communication interruption rate for the system, respectively. Finally, two numerical examples are given to verify the effectiveness of the proposed scheme.

Novel criteria for exponential stability in mean square of stochastic delay differential equations with Markovian switching

Novel criteria for exponential stability in mean square of stochastic delay differential equations with Markovian switching

Sampled-Data H∞ Dynamic Output-Feedback Control for NCSs With Successive Packet Losses and Stochastic Sampling.

The problem of sampled-data H∞ dynamic output-feedback control for networked control systems with successive packet losses (SPLs) and stochastic sampling is investigated in this article. The aim of using sampled-data control techniques is to alleviate network congestion. SPLs that occur in the sensor-to-controller (S-C) and controller-to-actuator (C-A) channels are modeled using a packet loss model. Additionally, it is assumed that stochastic sampling follows a Bernoulli distribution. A model is established to capture the stochastic characteristics of both the SPL model and stochastic sampling. This model is crucial as it allows us to determine the probability distribution of the sampling interval between successive update instants, which is essential for stability analysis. An exponential mean-square stability condition for the constructed equivalent discrete-time stochastic system, which also guarantees the prescribed H∞ performance, is established by incorporating probability theory. The desired controller is designed using a step-by-step synthesis approach, which may offer lower design conservatism compared to some existing methods. Finally, our designed approach using a networked F-404 engine system model is validated and its merits relative to existing results are discussed. The proposed method is finally validated by employing a networked model of the F-404 engine system. Furthermore, the advantages of our method are presented in comparison to previous results.

Dynamic protocol-based sliding mode control for nonlinear semi-Markovian jump systems with deterministic switching

This study investigates the sliding mode control for semi-Markov jump systems with dynamic self-triggered protocol. Utilizing an average dwell time strategy, the variation of semi-Markov chain is regulated by a deterministic switching signal. To improve transmission efficiency and achieve better control performance, a dynamic self-triggered protocol is developed, which predicts the next triggered time based on the current sampled data, obviating the need for dedicated hardware to continuously monitor system states and eliminating the Zeno phenomenon. A sliding mode controller related to the self-triggered protocol is proposed, which ensures the finite-time reachability. Based on the proposed self-triggered protocol and Lyapunov theory, a sufficient criterion is established to guarantee mean-square exponential stability under partial unknown transition rates. Finally, the effectiveness of the proposed method is verified through simulation examples.

Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques

In this paper, we focus on stochastic delay differential equations in the G-framework (G-SDDEs). We introduce the practical stability to examine whether the performance of G-SDDE near an unstable equilibrium point is acceptable. We establish a new generalized Gronwall inequality based on which we prove the practical mean-square (PMS) exponential stability of G-SDDE. We also establish the stability equivalence between the discrete and the continuous EM approximations for G-SDDE and then show that the continuous EM approximation can preserve the PMS exponential stability of G-SDDE. One numerical experiment is conducted to confirm our theoretical results.

Parameterization to fault detection filtering for Itô stochastic T‐S fuzzy systems

AbstractThis article focuses on the fault detection filtering problem for Itô stochastic Takagi–Sugeno (T‐S) fuzzy systems. In terms of line integral Lyapunov function, a sufficient condition of exponential stability in mean square and extended dissipativity for the systems under consideration is established which has less conservatism than the one based on quadratic Lyapunov function. The obtained sufficient condition is nonlinear, which makes the synthesis of fault detection filter being difficult and challenging. By choosing general matrix variables and constructing the appropriate orthogonal complement matrices, the nonlinear sufficient condition can be converted into linear one ingeniously via utilizing Finsler's lemma twice. Thus, the fault detection filter can be developed by virtue of parameterization. It should be pointed out that our filter determined by the parameterization approach includes the one obtained by the equivalent transformation method as a special case. Finally, we demonstrate the feasibility and superiority of our proposed approach through three numerical examples.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Correction to: On exponential stability in mean square of nonlinear delay differential equations with Markovian switching

Correction to: On exponential stability in mean square of nonlinear delay differential equations with Markovian switching

Stability Analysis and Synthesis for Networked Systems With Noisy Sampling Intervals, Random Transmission Delays, and Packet Dropouts

In this article, we study the stability analysis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller synthesis problems for networked systems with random transmission delays and packet dropouts that are subject to noisy sampling intervals. The sampling errors and transmission delays are described by an independent and identically distributed sequence of continuous random variables and the transmission delays are assumed to be smaller than the noisy sampling intervals. First, a closed-loop discrete-time stochastic framework for networked system that allows investigating noisy sampling intervals, random transmission delays and packet dropouts simultaneously is established. To render the discrete-time stochastic system suitable for stability analysis and synthesis, an equivalent yet tractable stochastic augmented model is then reformulated with the help of matrix exponential computation. Based on this augmented model, a stability condition involving the expectation of a nonlinear and random coupling matrix is derived. By recurring to the law of total expectation and Kronecker product operation, the expectation operation of the coupling matrix subject to high nonlinearity and multiple randomness is decoupled. Subsequently, a controller algorithm is designed such that the exponential mean-square stability of the original discrete-time stochastic system with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance is guaranteed. Finally, an example is provided to illustrate the effectiveness of the controller design algorithm.

Dissipativity-based control for networked control systems under bilateral Round-Robin protocols and denial-of-service attacks

A dissipativity-based control strategy adopting bilateral Round-Robin (RR) protocols for networked control systems (NCSs) suffering from denial-of-service (DoS) attacks is investigated in this work. To save limited network resources in multi-packet transmission scenarios, RR protocols are adopted for coordinating the node access on bilateral (i.e., sensor-to-controller and controller-to-actuator) channels. Subsequently, the NCSs integrating considerations of bilateral RR protocols and DoS attacks are further described as the switched time-delay model. The sufficient stability condition and controller design criterion are derived by using Lyapunov theory to ensure the closed-loop exponential mean-square stability and (Q,S,R) dissipative performance under fragile network environment. Furthermore, to maximize the tolerable system delay and reduce the conservativeness of proposed results effectively, an optimization algorithm is also proposed. Finally, the superiority and feasibility of the proposed methods are verified through two practical examples.

Global exponential stability of nonlinear delayed difference systems with Markovian switching

This work addresses the global exponential stability of nonlinear delayed discrete-time systems with Markovian switching. By a novel approach, some explicit criteria for the exponential stability in mean square of such systems are derived. An application to discrete-time neural networks is presented.

Exponential mean-square stabilization control for cyber-physical systems under random DoS attacks and transmission delay

Exponential mean-square stabilization control for cyber-physical systems under random DoS attacks and transmission delay

FlexRay protocol based distributed nonfragile dissipative filtering of state-saturated switched stochastic systems

ABSTRACT This article concentrates on the finite-time nonfragile distributed dissipative filtering issue for time-varying switched stochastic systems (SSSs) with state saturations over wireless sensor networks based on FlexRay communication protocol. To effectively deal with the resource restriction problem of the public communication network and energy consumption of the sensor nodes, the FlexRay communication protocol, including the Round-Robin protocol (RRP) and weighted try-once-discard protocol (WTODP), is introduced to schedule the data transmission of each sensor node. In addition, the phenomenon of randomly occurring gain variations (ROGVs) of filter parameters, characterised by the Bernoulli distributed random variables, is taken into consideration for the implementation of desired filter. A sufficient condition under the average dwell time (ADT) restriction is presented to guarantee the mean-square exponential stability and stochastically dissipative property of the augmented filtering error system (AFES) in a finite horizon. Moreover, the gains of the dissipativity-based filters are achieved by solving recursive linear matrix inequalities (RLMIs). Finally, an illustrative example is provided to exhibit the effectiveness of the designed filter.

On exponential stability in mean square of nonlinear delay differential equations with Markovian switching

Abstract This paper addresses the exponential stability of nonlinear delay differential equations with Markovian switching. Drawing upon the comparison principle, we introduce the explicit criteria for achieving the exponential stability in mean square (sense). These criteria are formulated in terms of the equation coefficients and the generator of the Markovian switching process. As a result, these criteria can be verified without needing to construct the Lyapunov functions, a departure from the conventional approach found in the Razumikhin-type theorems. The paper includes an illustrative example and also demonstrates an application to the switched neural networks.

Fuzzy $\mathcal {H}_{\infty }$ Control of Semi-Markov Jump Singularly Perturbed Nonlinear Systems With Partial Information and Actuator Saturation

This paper focuses on the fuzzy control problem for a class of semi-Markov jump singularly perturbed nonlinear systems with actuator saturation. Nonlinearities in the underlying systems are tackled with the Takagi-Sugeno fuzzy model. As distinct from the previous achievements, the case that the semi- Markov kernel with partially known information is taken into account such that the underlying systems can be extended to a wider scope. Given that actuator saturation is ubiquitous in engineering systems, the convex hull method is embraced to address this circumstance. To reduce the conservativeness of the obtained results, on the basis of Lyapunov stability theory and LaSalle's invariance principle, some criteria related to the sojourn time are presented. Next, the mean-square exponential stability of the underlying system is obtained based on the derived results. Finally, further experiment to verify the feasibility of the proposed methodology is given by a tunnel diode circuit model.

A Novel Approach to Discriminate Mean-Square Exponential Stability of Hybrid Stochastic Delay Differential Systems

A Novel Approach to Discriminate Mean-Square Exponential Stability of Hybrid Stochastic Delay Differential Systems

Stability and stabilization analysis of periodic switching stochastic systems based on Lyapunov function with continuous time-varying matrix polynomials

In this paper, a Lyapunov function with continuous time-varying Lyapunov matrix polynomials is constructed to ensure the exponential stability in mean square of a periodic switched linear stochastic system, where the Lyapunov matrix of this Lyapunov function is no longer a constant matrix, but a continuous time-varying matrix polynomial. Then, based on this stability study, we design an aperiodic intermittent control for unstable periodic switching stochastic systems to solve the influence of unstable subsystems and switching rules on stability, and the corresponding control gains are continuous time-varying matrix polynomial. Finally, an example is demonstrated to illustrate the effectiveness of the proposed control strategy.

Exponential Stability of uncertain functional differential equations

In this paper, we study a class of non-linear uncertain functional differential equations driven by canonical Process that is the counterpart of Wiener process in the framework of uncertain theory. By using a novel approach, some new and exhibit criteria for the exponential stability in mean square of the considered equations is obtained. Lastly, some examples are investigated to illustrate the theory.

QoS-Dependent Event-Triggered Control for UAVs on Cognitive Radio Networks Subject to Deception Attacks

Based on cognitive radio (CR) networks, this paper considers event-triggered control for unmanned aerial vehicle (UAV) systems subject to deception attacks. Two states (ON and OFF) are switched in CR networks. For the switched model, a new Quality of Service (QoS)-dependent event-triggered scheme (ETS) is proposed over CR networks under deception attacks. For a non-ideal QoS, more sensitive trigger parameters are required against deception attacks. For an ideal QoS, less sensitive trigger parameters are adjusted to reduce data transmissions. Based on the QoS-dependent ETS, a new switched system is modeled subject to deception attacks. By constructing the Lyapunov functional, the criteria are obtained to guarantee the exponential mean-square stability of UAV systems and the desired <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{\infty }$</tex-math></inline-formula> performance. Moreover, an algorithm is developed to adjust the parameters of QoS-dependent ETS according to the QoS of CR network. Finally, an UAV system is utilized to show the effectiveness of the proposed approach.