Sufficient Conditions For Finite-time Boundedness Research Articles

Improved filtering of interval type-2 fuzzy systems over Gilbert-Elliott channels

This study is concerned with the filtering problem for networked interval type-2 (IT2) fuzzy systems in the presence of a time-varying saturation function. Different from the existing Bernoulli-type/Gilbert-Elliott packet loss over the unreliable medium, a generalized Gilbert-Elliott model is presented to describe the data transmission follows a two-state nonhomogeneous Markov process, whose transition probabilities are time-varying. For the purpose of mitigating the impacts of abnormal information, a novel filter in the presence of saturation function is constructed, in which the saturation level is dynamically updated along with the estimation errors. On the basis of Lyapunov theory, sufficient conditions for finite-time boundedness of IT2 fuzzy systems are devised. In the end, a simulation example is exploited to show the effectiveness of the above-derived results.

Observer-based finite-time asynchronous sliding mode control for Markov jump systems with time-varying delay

The issue of finite-time sliding mode control (SMC) is studied for a class of Markov jump systems, in which parameter uncertainties, external disturbances and time-varying delay are considered. Firstly, a suitable observer-based SMC law is devised so that state trajectory of the system can reach the designed sliding mode surface in finite-time, the gain of the controller is asynchronous to the mode of original system. Meanwhile, the sufficient conditions of finite-time boundedness in the sliding phase and reaching phase are derived by the time partition strategy. Moreover, the gains of the observer and the observer-based controller will be acquired by using the linear matrix inequalities tool. In fine, emulation products are used to confirm the merits of the SMC strategy.

Finite-time [formula omitted] and [formula omitted] boundedness for nonlinear singular switched positive systems with D-perturbations

The article studies the positivity, finite-time L1 boundedness and finite-time L∞ boundedness for nonlinear singular switched positive systems(NSSPSs) with D-perturbations. Firstly, a necessary and sufficient positivity condition is presented for NSSPSs by singular value decomposition approach. Then, considering the disturbance signal in the form of norm bounded integrable signal, based on average dwell time and co-positive Lyapunov function approach, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L1-gain performance, the result of finite-time L1 boundedness is presented for the considered system. In addition, considering the disturbance signal in the form of uniformly bounded signal, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L∞-gain performance, the result of finite-time L∞ boundedness is presented for the considered system. Finally, the correctness and effectiveness of the results are verified with four given examples.

Passive analysis and finite-time anti-disturbance control for semi-Markovian jump fuzzy systems with saturation and uncertainty

This paper mainly addresses the issue of passivity for semi-Markovian jump fuzzy systems (S-MJFSs) with saturation and uncertainty and analyzes the finite-time performance. Compared with existing research results, the passivity problem of semi-Markovian jump system (S-MJS) with mixed disturbances is proposed, and time-delay, parameter uncertainty are also considered in the close-loop systems. Takagi-Sugeno (T-S) fuzzy strategy is used to deal with finite-time nonlinear problem. Firstly, the sufficient condition of finite-time boundedness for S-MJFSs is proposed by the derivation and transformation of matrix inequality. Then, disturbance observer based control (DOBC) and passive control are combined to address the robust passive problem. Furthermore, finit-time passive controller is solved to guarantee the control requirements of uncertain S-MJFSs. Finally, the results are applied in the practical system model and the feasibility of the results is verified.

Robust finite-Time control and reachable set estimation for uncertain switched neutral systems with time delays and input constraints

This work focuses on robust finite-time fault-tolerant control and reachable set estimation for uncertain switched neutral systems subject to time delays as well as input constraints. There are few attempts to investigate robust finite-time boundedness and reachable set estimation for uncertain switched neutral systems. At the same time, input-output finite-time stability is also investigated. Compared with the existing studies, this system has wider application. A dynamic output feedback nonlinear controller is researched. An augmented closed-loop system is provided. Moreover, the sufficient conditions of finite-time boundedness, reachable set estimation and input-output finite-time stability for the closed-loop system are obtained in the framework of linear matrix inequalities via piecewise Lyapunov function. Ultimately, two examples are provided to demonstrate this validity of this approach in this paper.

Finite-time H ∞ control for stochastic Markovian jump systems with time-varying delay and generally uncertain transition rates

This paper considers the finite-time control problem for Markovian jump systems (MJSs) with time-varying delay and generally uncertain transition rates (GUTRs). Based on Lyapunov-Krasovskii functionals and free-weight matrices, some sufficient conditions for finite-time boundedness and finite-time boundedness of MJSs are derived in the presence of external disturbances and It-type stochastic disturbances. A state feedback controller is proposed to achieve finite-time boundedness performance. By applying linear matrix inequalities (LMIs), the parameterisation of the controller is converted to a convex optimisation problem. Finally, a practical example demonstrates the effectiveness of the proposed method.

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

This paper is concerned with the finite-time boundedness of two dimensional (2-D) positive continuous-discrete systems in Roesser model. By constructing an appropriate co-positive type Lyapunov function, sufficient conditions of finite-time stability for the nominal 2-D positive continuous-discrete system are established. Sufficient conditions of finite-time boundedness for the addressed system with external disturbances are also proposed. The proposed results are then extended to uncertain cases, where the interval and polytopic uncertainties are considered respectively. Finally, three examples are provided to illustrate the effectiveness of the proposed results.

Time-varying delay-dependent finite-time boundedness with [formula omitted] performance for Markovian jump neural networks with state and input constraints

This work focuses on time-varying delay-dependent finite-time boundedness with H∞ performance for Markovian jump neural networks with state and input constraints. This is the first try to study finite-time boundedness with H∞ performance for Markovian jump neural networks with state and input constraints. There are disturbance input and system state with bounded peaks in the nonlinear system. In contrast to the existing study results, the studied system can be applied to a wider range. The purpose is to obtain less conservative conditions on finite-time H∞ performance for Markovian jump neural networks with time-varying delay. Sufficient conditions of finite-time boundedness with H∞ performance are collected by stochastic Lyapunov function. Linear matrix inequalities are utilized to obtain analysis results. Eventually, an example is provided to illustrate the validity of the addressed method.

Finite-time Stabilization for Uncertain Neural Networks With Time-varying Delay

In this paper, the problems of finite-time boundedness and control design for uncertain neuralnetworks with time-varying delay is considered. By constructing Lyapunov-Krasovskii function and using thematrix inequality method, sufficient conditions for finite-time boundedness of a class of neural networks withtime-varying delay are established. Then, we proposed a criterion to ensure that the neural networks with timevarying delay is finite-time stabilizable. A numerical example is given to verify the validity of the results.

Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

Finite-time non-fragile filtering for nonlinear networked control systems via a mixed time/event-triggered transmission mechanism

This paper is aimed at investigating the problem of mixed time/event-triggered finite-time non-fragile filtering for nonlinear networked control systems with delay. First, a fuzzy nonlinear networked control system model is established by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, the designed non-fragile filter resolves the filter parameter uncertainties and uses different membership functions from the IT2 T-S fuzzy model. Second, a novel mixed time/event-triggered transmission mechanism is proposed, which decreases the waste of network resources. Next, Bernoulli random variables are used to describe the cases of random switching mixed time/event-triggered transmission mechanism. Then, the error filtering system is designed by considering a Lyapunov function and a sufficient condition of finite-time boundedness. In addition, the existence conditions for the finite-time non-fragile filter are given by the linear matrix inequalities (LMIs). Finally, two simulation results are presented to prove the effectiveness of the obtained method.

Decentralized finite-time control for linear interconnected fractional-order systems with input saturation

This paper investigates decentralized finite-time boundedness and control problems for a linear interconnected fractional-order system with input saturation. By Lyapunov function, generalized Gronwall inequality, and fractional-order Caputo derivative inequality, sufficient conditions for finite-time boundedness of the linear interconnected fractional-order system are established. Both the decentralized state feedback controller and the decentralized output feedback controller are designed to guarantee the finite-time boundedness of the closed-loop system, and the seeking methods of controller gains are given by solving linear matrix inequalities. Finally, two simulation examples are employed to illustrate the effectiveness of the obtained results.

Finite-Time Non-Fragile Extended Dissipative Control of Periodic Piecewise Time-Varying Systems

This paper studies the problem of finite-time non-fragile extended dissipative control for the periodic piecewise time-varying systems. First, based on the time-varying Lyapunov matrix and the matrix polynomial condition, a sufficient condition of finite-time boundedness for periodic piecewise time-varying subsystem is derived, and the finite-time extended dissipative performance is then analyzed. Furthermore, considering two types of time-varying controller perturbations, the non-fragile controllers are developed, which can guarantee the finite-time boundedness of periodic piecewise time-varying systems and satisfy the extended dissipative performance at the same time. Finally, numerical examples demonstrate the effectiveness of the proposed methods.

Finite-time boundedness and chaos-like dynamics of a class of Markovian jump linear systems

This paper investigates dynamic properties of a class of stochastic Markovian jump linear systems. Firstly, we introduce quasi-alternative Markovian jump linear switching systems with both stable and unstable subsystems. Then, we provide sufficient conditions of finite-time boundedness by using Lyapunov methods and system future analysis. These presented conditions guarantee the existence of boundary within a given time interval. Next, we further analyse an useful dynamic property, named as finite-time chaos-like property, based on boundedness and stationary distribution characteristics. Finally, a detailed example is presented to illustrate our main results.

On the finite-time boundedness of linear systems

This paper deals with the finite-time boundedness (FTB) of linear time-varying (LTV) systems; in this context, the novel contribution of our work goes in several directions. The first result is a sufficient condition for FTB when the plant input is generated by an exo-system; it is worth noting that constant, norm bounded signals, which most part of the previous literature has considered so far, belong to such class of inputs. To this regard, it is possible to compare our result with the existing literature, which shows that our approach yields less conservative conditions. The second result provided in the paper, is a sufficient condition for FTB when the input belongs to L2, the class of square integrable signals, which have never been considered so far. In both cases, the proposed results require the solution of a feasibility problem constrained by differential linear matrix inequalities (DLMIs). A third contribution of the paper proves that, from the system-theoretic point of view, the obtained FTB conditions can be interpreted in terms of the norm of a suitable input–output operator. As a consequence of this fact, we are able to find alternative and equivalent conditions for FTB, both for the exogenous and the L2 cases, which are based on the solution of differential Lyapunov equations (DLEs), which are much more efficient from the computational point of view. The DLMI-based condition, however, is fundamental to solve the design problem, which is also investigated in the paper. Some examples show that the proposed technique is less conservative with respect to the previous literature, when exogenous inputs are considered, and its effectiveness when L2 signals are considered. Moreover, one example is devoted to show that the analysis approach, based on the solution of DLE, is much more efficient from the computational point of view with respect to the one based on DLMIs; finally the last example investigates the application of the state feedback control technique.

Formula omitted] finite-time stabilization for positive semi-Markovian switching systems

This paper investigates robust finite-time stabilization scheme for positive semi-Markovian switching systems (S-MSSs). Semi-Markovian process (SMP), external disturbances, and transient performances at a finite-time level may appear in a controlled system. A more general system model for S-MSSs that covers Markovian switching systems (MSSs) as a special case is suitable for describing some complex systems that are subject to random abrupt changes in structure and parameter. The main motivation for this is that finite-time problems can be used to describe the transient performance of practical industrial control processes. First, under the framework of stochastic semi-Markovian Lyapunov functions theory, some sufficient conditions for finite-time boundedness (FTBs) and L1 FTBs criteria for positive S-MSSs are proposed for all admissible disturbances. Then, a novel L1 finite-time controller design method that employs the gain matrix decomposition method is presented to reduce some conservativeness, thereby guaranteeing that the resulting closed-loop system (RLCS) could achieve positivity, FTBs, and attain a prescribed L1 noise attenuation performance index in standard linear programming (LP). Finally, a practical example is introduced to show the effectiveness of the main theory

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen’s inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Results on finite‐time boundedness and finite‐time control of non‐linear quadratic systems subject to norm‐bounded disturbances

The present study investigates the synthesis of sufficient conditions for finite-time boundedness and stabilisation of non-linear quadratic systems with exogenous disturbances. For this purpose, the usefulness of combining the notion of annihilator with a version of Finsler's lemma has been investigated. The obtained design conditions are expressed in terms of a set of state-dependent linear matrix inequalities. Several numerical examples are given to show the effectiveness of the authors' approach.

Nonfragile Finite-Time Extended Dissipative Control for a Class of Uncertain Switched Neutral Systems

This paper is concerned with finite-time extended dissipative analysis and nonfragile control for a class of uncertain switched neutral systems with time delay, and the controller is assumed to have either additive or multiplicative form. By employing the average dwell-time and linear matrix inequality technique, sufficient conditions for finite-time boundedness of the switched neutral system are provided. Then finite-time extended dissipative performance for the switched neutral system is addressed, where we can solve H∞, L2-L∞, Passivity, and (Q,S,R)-dissipativity performance in a unified framework based on the concept of extended dissipative. Furthermore, nonfragile state feedback controllers are proposed to guarantee that the closed-loop system is finite-time bounded with extended dissipative performance. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.

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.