Conditions For Finite-time Stability Research Articles

Finite-time stabilization of input-delay switched systems

In the framework of digital control, finite-time stabilization of input-delay switched systems with saturating actuators is investigated. Digital state feedback controllers (DSFC) and digital output feedback controllers (DOFC) are proposed to make input-delay switched systems finite-time stable for the cases that states are available or unavailable. Sufficient conditions for finite-time stability (FTS) of the resultant closed-loop systems are also presented. A constructive way is used to proof the main results, which is constructing an exact comparison function. Numerical examples are employed to verify the efficiency of the methods proposed in this paper.

Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.

Sufficient Stability Conditions for Polynomial Systems

For polynomial systems of perturbed equations of motion, a new estimate of the Lyapunov function along the solutions of the system equations is proposed. Based on the estimate, the conditions for Lyapunov stability, practical stability, and finite-time stability for large initial perturbations are established.

Neural-Adaptive Finite-Time Formation Tracking Control of Multiple Nonholonomic Agents With a Time-Varying Target

This paper investigates the leader-following formation tracking problem (FTP) for multiple nonholonomic agent systems (MNASs) in the presence of external disturbances and parametric uncertainties, where both the kinematics and dynamics of the agents are taken into consideration. A novel finite-time distributed controller-estimator algorithm (DCEA) is designed to handle such a challenging problem. Based on Lyapunov stability method, the sufficient conditions for finite-time stability of the closed-loop system are derived. Finally, the simulation results are presented to demonstrate the effectiveness and the robustness of the proposed DCEA.

Finite-Time Stability of Switched Linear Time-Delay Systems Based on Time-Dependent Lyapunov Functions

In this paper, finite-time stability of switched linear time-delay systems has been addressed. By constructing a class of time-dependent common (multiple) Lyapunov functions, new explicit conditions for finite-time stability of the system under arbitrary switching and average dwell-time switching are established respectively. Compared with most of existing results in the literature, our results are easily verifiable by solving several linear matrix inequalities rather than complex matrix Riccati differential equations. The effectiveness of the proposed method is demonstrated by numerical examples.

Adaptive Finite-Time Control for Half-Vehicle Active Suspension Systems with Uncertain Dynamics

The finite-time control design problem of half-vehicle active suspension systems with uncertain dynamics and external disturbances is investigated in this article. The unknown functions, which caused by uncertain parameters and unknown dynamics, are approximated with help of neural networks. An extended Lyapunov condition of finite-time stability is employed to achieve the control of the vertical and pitch motions more quickly. Then, assisted by the practical finite-time theory, the finite-time controller is proposed. It can ensure that half-vehicle active suspension systems achieve the stability in a finite time and the ride comfort can be enhanced. In addition, the developed adaptive finite-time control approach is performed to half-vehicle active suspension systems. By comparing analysis of simulation results, the validity of the established scheme is demonstrated and the performance of half-vehicle active suspension systems is exhibited.

New Results on Finite-Time Stability and Stabilization of Switched Positive Linear Time-Delay Systems

In this paper, the problems of finite-time stability and stabilization for switched positive linear time-delay systems under mode-dependent average dwell time (MDADT) are investigated. By proposing a novel multiple piecewise copositive Lyapunov-Krasovskii functional, new results on the sufficient conditions of finite-time stability are obtained. In order to solve the limitation of the multiple piecewise copositive Lyapunov-Krasovskii functional on designing controllers, a novel linear combinatorial copositive Lyapunov-Krasovskii functional is constructed, this provides a possibility for the numerical construction of the controller. Then by using state feedback controller, the finite-time stabilization is achieved. Finally, some simulation results are given to show the advantages of our methods.

Robust Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability

In this paper we propose a new family of continuous-time optimization algorithms based on discontinuous second order gradient optimization flows, with finite-time convergence guarantees to local optima, for locally strongly convex time-varying cost functions. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of time-varying differential inclusions. We then prove the convergence of these second-order flows in finite-time. We show the performance of these flows on a time-varying quadratic cost and on the nonlinear time-varying Rosenbrock function.

Annular finite-time stability analysis and synthesis of stochastic linear time-varying systems

In this paper, we investigate some finite-time control problems for stochastic linear time-varying systems, described by an Itô type differential equation. In particular, the annular stochastic finite-time stability control problem is dealt with. In this context, it is required that the norm of the state variables remains bounded between an inner and an outer ellipsoid, during a finite-interval of time. The first contribution of the paper consists of two sufficient conditions for stability, which are derived by exploiting an approach based on time-varying quadratic Lyapunov functions. The first condition requires the solution of two generalised differential Lyapunov equations; the latter the existence of a feasible solution to a pair of differential linear matrix inequalities. As particular cases, we obtain sufficient conditions for stochastic finite-time stability (in this last case, the lower ellipsoid collapses to the origin). From the analysis conditions, a sufficient condition is derived for the annular stochastic finite-time stabilisation via both state and output feedback. Some numerical examples illustrate the application of the proposed methodology and show that our approach attains less conservative results than those obtainable with the existing literature. Moreover, an application of the annular stochastic finite-time stability approach to the stabilisation problem of a satellite with respect to the geomagnetic field is presented.

Adaptive Finite-Time Attitude Tracking of Quadrotors With Experiments and Comparisons

The finite-time attitude control of quadrotor unmanned aerial vehicles (UAVs) subject to external disturbances with unknown bound is investigated in this paper. First, an adaptive multivariable finite-time stabilizing control algorithm for second-order multivariable systems is developed based on the improved supertwisting and the equivalent control algorithms. Furthermore, the finite-time stability conditions are derived via the Lyapunov technique. The remarkable feature of the developed algorithm is to eliminate the overestimation of the control gains without loss of the sliding motion. Then, the proposed algorithm is applied for quadrotor UAVs to solve the finite-time attitude-tracking problem. Finally, a comparison of the proposed multivariable algorithm with its scalar counterpart is presented and validated both by simulation and experiment results.

Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

Security control of cyber–physical system based on switching approach for intermittent denial-of-service jamming attack

In this study, the effects caused by intermittent denial-of-service jamming attack (I-DoS-JA) on different communication channels and communication topology transformations have been deeply analyzed. According to the analyzation, each different communication topology is taken as a subsystem of switching system. Based on switching system, finite-time nonlinear system robust stability conditions are derived. Both the theoretical deduction and example simulation have corroborated that this approach has special effective in resisting the intermittent DoS attack.

Finite-time stability and stabilisation of singular discrete-time linear positive systems with time-varying delay

ABSTRACTIn this paper, the problem of finite-time stability and stabilisation for positive singular discrete-time linear systems with time-varying delay is investigated. We first present novel delay-dependent sufficient conditions for positivity and finite-time stability of the unforced systems. We then apply the obtained results to solve finite-time stabilisation problem of the considered systems. The sufficient conditions for the positivity and finite-time stabilisable of such systems are formulated in terms of a standard linear programming (LP) problem. Numerical examples are provided to illustrate the effectiveness and advantages of our results.

New finite-time stability conditions of linear discrete switched singular systems with finite-time unstable subsystems

The finite-time stability problem of linear discrete switched singular systems with finite-time unstable subsystems is studied in this paper. By using dynamic decomposition technique, the original switched singular systems can be transformed into equivalent one that is a reduced-order switched normal systems. For linear discrete switched singular systems, based on the mode-dependent average dwell time (MADAT) switching signal, new sufficient conditions are presented to guarantee the considered systems with finite-time unstable subsystems being finite-time stability, finite-time bounded. At last, two numerical examples is employed to verify the efficiency of the preceding method.

Finite-time stability for fractional-order complex-valued neural networks with time delay

This paper explores the finite-time stability of fractional-order complex valued neural networks with time delay. By employing Laplace transform and the properties of Mittag-Leffler function, a lemma of exponent stability is developed to derive the finite-time stability conditions. Further, by using the proposed lemma and the techniques of inequalities, the finite-time stability of fractional-order complex-valued neural networks with time delay is analyzed with and without a controller. In addition, some sufficient conditions are proposed to analyze the finite-time stability of the fractional-order complex-valued neural networks and the setting time for stability is also estimated. Finally, two examples are used to verify the validity and feasibility of the proposed criteria.

New Lyapunov conditions of stochastic finite-time stability and instability of nonlinear time-varying SDEs

In this paper, we further consider the problem of stochastic finite-time stability and instability of nonlinear stochastic differential equations (SDEs) with time-varying drift and diffusion terms. The contributions of the paper are highlighted as follows. Some new conditions via multiple Lyapunov functions are given for stochastic finite-time stability of nonlinear time-varying SDEs. Compared with the existing results on stochastic finite-time stability, the constraint of the differential operator is further relaxed in this paper, which enable us to construct the Lyapunov functions much more easily in applications for nonlinear time-varying SDEs. In addition, a stochastic finite-time instability theorem is proposed, and it shows the necessity of in the proposed conditions of stochastic finite-time stability. Some examples are presented to illustrate the new results.

Improved Approach for Finite-Time Stability of Nonlinear Fractional-Order Systems With Interval Time-Varying Delay

In this brief, we propose an approach based on the Laplace transform and “inf-sup” method for studying finite-time stability of fractional-order systems (FOS) with time-varying delay and nonlinear perturbation. Based on the proposed approach, we establish new delay-dependent conditions for finite-time stability of FOS with interval time-varying delay. The conditions are presented in terms of the Mittag-Leffler function and linear matrix inequalities, which are less conservative and easier to verify than the existing ones. The proposed method is also applicable for finite-time stability of linear uncertain time-delay FOS. Numerical example are given to show the validity and effectiveness of the proposed results.

An Observer-Based Output Feedback Controller for the Finite-Time Stabilization of Markov Jump Linear Systems

In this letter, we investigate the finite-time output feedback control problem for continuous-time Markov jump linear systems. In this context, the first result is a sufficient condition for stochastic finite-time stability, requiring the solution of a feasibility problem constrained by differential linear matrix inequalities. Afterward, we consider the stabilization problem via output feedback dynamical controllers. The usual machinery pursued in the deterministic case would lead to stabilization conditions depending on differential bilinear matrix inequalities, that cannot be solved in practice. Therefore, a different methodology, based on the separation approach provided by Amato et al. , is exploited to design an observer-based output feedback controller, which can be computed by solving an optimization problem depending on linear constraints. A non-trivial application example, involving the finite-time stabilization of the longitudinal dynamics of a helicopter, is presented in order to illustrate the effectiveness of the proposed technique.

Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality

In this article, a new integral inequality based on a free-matrix for bounding the integral ∫abẋT(u)Rẋ(u)du has been proposed. The new inequality and appropriated Lyapunov–Krasovskii functional play key roles for deriving finite-time stability criteria of linear systems with constant and continuous non-differentiable time-varying delays. The new sufficient finite-time stability conditions have been proposed in the forms of inequalities and linear matrix inequalities. In addition, we apply the same procedure as done for deriving finite-time stable criteria but using Wirtinger-based inequality instead of our new inequality and compare these criteria with other works. At the end, two numerical examples are presented to show that the proposed criteria are practicable for linear systems with non-differentiable delay. Criteria using proposed integral inequality yield better results than the other works for linear system with constant delay. However, results using Wirtinger inequality are less conservative when time-varying delay is considered.

A finite-time sliding mode control for hypersonic vehicle

In this paper, a finite-time control strategy based on back-stepping method combining with a terminal sliding mode control (TSMC) and a nonlinear disturbance observer (NDO) is proposed for the longitudinal dynamic model of hypersonic vehicle (HV). Firstly, the model of HV is transformed into two strict feedback subsystem: the mismatched subsystem of altitude and the matched subsystem of velocity. Then, the TSMC and back-stepping method is incorporated to cope with the unmatched issue in the HV altitude subsystem. In addition, a NDO based on a finite-time-convergent differentiator (FD) is proposed to estimate the lumped disturbances. The finite-time stability condition of the system is established via the Lyapunov theory. Finally, the robustness and effectiveness of the method are verified by simulations.