Conditions For Finite-time Boundedness Research Articles

Finite-time non-fragile passivity control for neural networks with time-varying delay

In this paper, the problem of finite-time non-fragile passivity control for neural networks with time-varying delay is studied. We construct a new Lyapunov–Krasovskii function with triple and four integral terms and then utilizing Wirtinger-type inequality technique. The sufficient conditions for finite-time boundedness and finite-time passivity are derived. Furthermore, a non-fragile state feedback controller is designed such that the closed-loop system is finite-time passive. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix inequalities (LMIs) using Matlab LMI toolbox. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed criteria.

Finite-time boundedness and dissipativity analysis of networked cascade control systems

In this paper, finite-time boundedness and dissipativity analysis for a class of networked cascade control systems (NCCSs) is investigated. The NCCS is defined with network-induced imperfections such as packet dropouts and time delays, and Bernoulli distributed white sequence is used to model a stochastic packet dropout case. Using the Lyapunov stability theory and linear matrix inequality (LMI) approach, we propose the sufficient conditions for finite-time boundedness and finite-time dissipativity of NCCS. Finally, the LMI-based conditions are applied on a practical power plant boiler–turbine system to show the effectiveness and applicability of the achieved results.

Novel results on robust finite-time passivity for discrete-time delayed neural networks

This paper presents some novel results on robust finite-time passivity for a class of uncertain discrete-time neural networks (DNNs) with time varying delays. Using the Lyapunov theory together with the zero inequalities, convex combination and reciprocally convex combination approaches, we propose the sufficient conditions for finite-time boundedness and finite-time passivity of DNN for all admissible uncertainties. The results are achieved by using a new Lyapunov-Krasovskii functional (LKF) with novel triple summation terms, several delay-dependent criteria for the DNN are derived in terms of linear matrix inequalities (LMIs) which can be easily verified via the LMI toolbox. Finally, numerical example with simulation scheme have been presented to illustrate the applicability and usefulness of the obtained results.

Finite-Time $H_{\infty }$ Filtering for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay and Norm-Bounded Uncertainties

In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are proposed and the filter gain matrices can be obtained by calculating a set of linear matrix inequalities. A numerical example is used to illustrate the effectiveness of the proposed approaches.

Finite-Time $$L_1$$ L 1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates

The paper deals with the problem of finite-time $$L_1$$L1 control for positive Markovian jump systems with partly known transition rates. Firstly, by constructing a linear co-positive Lyapunov function, sufficient conditions for finite-time boundedness and $$L_1$$L1 finite-time boundedness of the open-loop system are developed. Then, an effective method is proposed for the construction of the state feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, two examples are given, which include a mathematical model of virus mutation treatment to illustrate the validity of the obtained results.

Finite-timeL1control for positive Markovian jump systems with constant time delay and partly known transition rates

The paper is concerned with finite-time L1control for positive Markovian jump systems with constant time delay and partly known transition rates. By constructing appropriate co-positive type Lyapunov function, sufficient conditions for finite-time boundedness and L1finite-time boundedness of the underlying system are firstly given. Based on the results obtained, a state feedback controller is designed such that the closed-loop Markovian jump system is positive and L1finite-time bounded. All the proposed conditions are given in linear programming. Finally, an example is given to demonstrate the validity of the main results.

Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

Finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching

This paper investigates the problem of finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching. Another set of useful regime-switching models has been given for both fixed transition probability Markov switching models and time-varying transition probabilities. Based on the knowledge of average dwell time and multiple Lyapunov function, a novel sufficient condition for finite-time boundedness of H∞ filtering is derived and the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.

A New Finite-Time Bounded Control of Stochastic Itô Systems with (x,u,v)-Dependent Noise: Different Quadratic Function Approach

This paper addresses the finite-time bounded control problem of linear stochastic systems with state, control input, and external disturbance-dependent noise ((x,u,v)-dependent noise for short). The notion of finite-time boundedness of linear stochastic systems is first introduced. Then a different quadratic function approach is proposed to give a sufficient condition for finite-time boundedness of such a class of systems, and its superiority to common quadratic approach is shown. Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. Finally, an example is employed to illustrate the effectiveness of our obtained results.

Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching

An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov–Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.

Finite-time boundedness and stabilisation of networked control systems with bounded packet dropout

In this paper, the finite-time boundedness and stabilisation problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilisation of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Finite-Time Boundedness Control of Time-Varying Descriptor Systems

This paper mainly studies a control problem of finite-time boundedness of time-varying descriptor systems. Firstly, a sufficient and necessary condition of finite-time stability is given, then a sufficient condition of finite-time boundedness for time-varying descriptor systems is given. Secondly, we analyze the finite-time boundedness control problem and design the finite-time state feedback controller; the controller is given based on LMIs for time-varying descriptor systems and time-varying uncertain descriptor systems, respectively. Finally, a numerical example is given to prove the effectiveness of the method.

Finite-Time Control of Networked Control Systems with Bounded Packet Dropout

In this paper, the finite-time boundedness and stabilization problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump liner systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilization of the underlying systems are derived via liner matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Finite‐Time Boundedness and Stabilization of Networked Control Systems with Time Delay

The finite‐time control problem of a class of networked control systems (NCSs) with time delay is investigated. The main results provided in the paper are sufficient conditions for finite‐time stability via state feedback. An augmentation approach is proposed to model NCSs with time delay as linear systems. Based on finite time stability theory, the sufficient conditions for finite‐time boundedness and stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

Robust finite-time H∞ control for a class of uncertain switched neutral systems

This paper investigates the robust finite-time H ∞ control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a sufficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H ∞ performance analysis for switched neutral systems is developed, and a robust finite-time H ∞ state feedback controller is proposed to guarantee that the closed-loop system is finite-time bounded with H ∞ disturbance attenuation level γ. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.