Finite-time Boundedness Analysis Research Articles

Finite-time filtering for fuzzy nonlinear semi-Markov jump systems with deception attacks and aperiodical transmission

This paper investigates finite-time event-triggered filtering problems for fuzzy nonlinear semi-Markov jump systems (S-MJSs) subject to deception attacks. First, an interval type-2 (IT2) fuzzy S-MJSs is presented that can capture parameter uncertainties, in which the stochastic behavior is described by semi-Markov process while the sojourn-time obeys non-exponential distribution. Second, we design an adaptive event-triggered mechanism (AETM) for IT2 fuzzy S-MJSs that can save network resources, in which the triggered parameter can be automatically adjusted with the error information rather than a fixed value. Third, a hidden-Markov model is employed to represent the asynchronous situation between the filter and system. Then, a new IT2 fuzzy filtering error system is modeled by taking the effects of random deception attacks and AETM into consideration. Moreover, finite-time boundedness (FTB) analysis and a filter design method are proposed. Finally, an example is given to verify the effectiveness of the finite-time event-triggered filtering algorithm.

Finite-time boundedness analysis and composite anti-disturbance control for uncertain semi-Markovian jump systems with time delay

Finite-time boundedness analysis and composite anti-disturbance control for uncertain semi-Markovian jump systems with time delay

Observer-based finite-time bounded analysis for switched inertial recurrent neural networks under the PDT switching law

In this note, the observer-based finite-time boundedness analysis issue for the switched inertial recurrent neural networks ( SIRNNs) is investigated deeply. The switching law, persistent dwell-time, with more generality and universality is employed. The first target is to develop a switched estimation system (SES) to obtain the states from the output of the researched open-loop SIRNNs. Thereafter, based on the before-mentioned SES, the resulting switched estimation error system (SEES) without the extrinsic disturbance, along with the closed-loop SIRNNs under state feedback controller are constructed. Furthermore, the sufficient conditions that the exponential stability for the SEES and the finite-time boundedness for the closed-loop SIRNNs are established simultaneously. The relevant estimator and controller gains are deduced by a straightforward decoupling manner. Ultimately, the feasibility of the method proposed is clarified and illustrated via a numerical example.

Takagi–Sugeno Model-Based Sliding Mode Observer Design for Finite-Time Synthesis of Semi-Markovian Jump Systems

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.

Finite-Time Boundedness and H∞ Control for Affine Switched Systems

For affine switched systems, the existence of multiple equilibria is related to subsystems owing to the affine terms, which makes asymptotic and finite-time stability analysis nontrivial. In this paper, the problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance. At first, the definition of FTB for affine switched systems is improved concerning the affine terms and multiple equilibria. Based on the FTB definition, sufficient conditions ensuring finite-time boundedness for affine switched systems under a prespecified state boundary are given. Then the results are extended to solve H∞ finite-time boundedness problem, in which the H∞ controllers are designed to guarantee the finite-time boundedness of affine switched system with H∞ performance. In our investigation, average dwell-time approach is employed to study the time-dependent constrained switching case. Finally, several numerical examples are given to illustrate the effectiveness of the proposed results.

Finite-time H∞ control for a chaotic finance system via delayed feedback

ABSTRACTThis paper is concerned with the finite-time control problem for a chaotic finance system subject to energy-bounded external disturbance via delayed feedback controller. Based on an augmented Lyapunov-like functional, the Wirtinger-based inequality and the novel finite-time boundedness analysis approach, a delay-dependent sufficient condition is proposed in terms of linear matrix inequalities such that the closed-loop error system is finite-time bounded with a prescribed performance level. By simple modification, the sufficient condition based on the standard control design is also obtained. Finally, simulation results are given to demonstrate the effectiveness and advantages of our proposed results.

Finite-time boundedness analysis and [formula omitted] control for switched neutral systems with mixed time-varying delays

This paper investigates the finite-time boundedness, observer-based finite-time stabilization, and H∞ control problems for a class of switched neutral systems with mixed time-varying delays and nonlinear perturbation. Using the delay-dependent Lyapunov–Krasovskii functional and the average dwell time technique, criteria to guarantee that the nonlinear switched neutral system is finite-time bounded are presented. Then, based on the matrix inequalities technology and the average dwell time approach, sufficient conditions of observer-based finite-time stabilization are established. Also, the observer-based feedback controller for the finite-time H∞ control problem is obtained. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.

Robust finite‐time H ∞ control for switched systems by using sojourn‐probability‐dependent method

This study deals with the problem of robust H ∞ finite-time boundedness analysis and design of finite-time H ∞ feedback control for discrete switched systems. By using sojourn probability information, a new kind of switched system model is proposed. Based on this model, sufficient conditions for the H ∞ finite-time boundedness are obtained by using Lyapunov functional method and the corresponding controllers are also designed. Moreover, when considering partially known probabilities and unknown system uncertainties, the analysis and design methods are also given. Finally, an example is given to illustrate the efficiency of the proposed method.

Finite-Time Boundedness Analysis of Memristive Neural Network with Time-Varying Delay

This paper considers the issue of the finite-time boundedness (FTB) of memristive neural network (MNN) with time-varying delay. It is known that the parameters of MNN are state dependent, the syste...

Finite-time boundedness analysis for a new multi-layer switched system with time-delay

In this paper, the finite-time boundedness problem of a multi-layer switched system subject to average dwell time switching signal, Markov jump and time-varying polytopic uncertainties is investigated. The sufficient conditions guaranteed the conclusion are shown in the form of linear matrix inequalities to ease the formulation, and the switched Lyapunov–Krasovskii approach is used in detail proofs. At last, an illustrative example is employed to demonstrate the efficiency of the main result.

Finite‐time boundedness of switched delay systems: the reciprocally convex approach

This study is concerned with the problem of finite-time boundedness analysis for switched delay systems with the average dwell time. By combining the Jensen inequality and the reciprocally convex approach, a sufficient condition is derived to guarantee the finite-time boundedness of switched linear systems subject to time-varying delays. It is shown that the obtained result can achieve better performance comparing with the previous ones. Finally, simulation examples are provided to demonstrate the theoretical results.

Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps

This paper is concerned with stochastic finite-time boundedness analysis for a class of uncertain discrete-time neural networks with Markovian jump parameters and time-delays. The concepts of stochastic finite-time stability and stochastic finite-time boundedness are first given for neural networks. Then, applying the Lyapunov approach and the linear matrix inequality technique, sufficient criteria on stochastic finite-time boundedness are provided for the class of nominal or uncertain discrete-time neural networks with Markovian jump parameters and time-delays. It is shown that the derived conditions are characterized in terms of the solution to these linear matrix inequalities. Finally, numerical examples are included to illustrate the validity of the presented results.

Finite-Time Boundedness Analysis for a Class of Switched Linear Systems with Time-Varying Delay

The problem of finite-time boundedness for a class of switched linear systems with time-varying delay and external disturbance is investigated. First of all, the multiply Lyapunov function of the system is constructed. Then, based on the Jensen inequality approach and the average dwell time method, the sufficient conditions which guarantee the system is finite-time bounded are given. Finally, an example is employed to verify the validity of the proposed method.

Finite time H∞ filtering for uncertain discrete-time switching systems

The concept of finite-time stability (FTS) has gained much attention from researchers in recent years, after the emergent utilization of linear matrix inequalities (LMIs) in the field of control systems. In this paper, FTS and finite-time boundedness (FTB) analysis and synthesis procedure for a ‘finite-time H∞ filter’ for discrete-time switching systems are presented. Assuming the external disturbance to be energy bounded, sufficient conditions for the designated H∞ filter-based system to be finite-time stable are proposed. Considering dwell-time switching, average and minimum dwell time in terms of ‘finite-time’ system parameters has been formulated. Furthermore, these results are extended to uncertain switching system, by assuming the switching system subject to norm-bounded parameter uncertainties. The intended filter design steps have been demonstrated for both certain and uncertain system models. A cost function is introduced and then a parametric optimization algorithm is devised to calculate optimal filter parameters and present the derived results in LMI form. Numerical design examples are presented at the end to demonstrate the results.

LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties

In this paper, the problem of finite-time boundedness (FTB) for neural networks with parameter uncertainties is studied. We extend the concept of FTB for neural networks. Based on the linear matrix inequality (LMI) technique, a sufficient condition is derived to guarantee FTB for uncertain neural networks. Besides, we also simply give a sufficient condition for certain systems. Finally, illustrative examples are given to demonstrate the validity of the proposed theoretical results.