Finite-time Stability Of Systems Research Articles

Average Consensus and Stability Analysis in Networked Dynamic Systems

This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is a high dimensional vector as a solution of the highly nonlinear first order dynamics with and without drift terms. This paper provides protocols for finitetime average consensus and finitetime stability of systems with controlled nonlinear dynamics innetwork under undirected fixed topology. Each node’s state is high Under the proposed interaction rules, agreements as a common average value or an average trajectory are reached, solving finitetime average consensus and the multisystem equilibrium is controlled leading to the finitetime stability of each system origin. Sufficient conditions are achieved using the Lyapunov techniques and the graph theory. In networked dynamic systems, the theoretical results of the paper cover a large class of underactuated autonomous systems as formation flight, multivehicle coordination, and heterogeneous multisystem behaviors. Some examples are introduced in simulation which approves the proposed protocols.

Fixed-time and finite-time stability of switched time-delay systems

This paper investigates fixed-time and finite-time stability of switched nonlinear time-varying time-delay systems. It is shown that by assuming these kinds of stability for each subsystem in the family, the similar properties can be ensured for the whole system under commutation with a sufficiently big (average) dwell time. The estimates on admissible dwell-time values are derived. Compared with existing results, the novelties of the obained results lie in that: (i) A class of Lyapunov–Krasovskii functionals with inde nite derivative is constructed for switched nonlinear time-delay systems, (ii) Average dwell time switching laws are designed for the fixed-time and finite-time stability of the systems, and (iii) The presented approach has potential applications in fixed-time and finite-time stability of other hybrid systems. The efficacy of the obtained results is illustrated by academic examples.

Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

In this article, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a time-varying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a second-order sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples.

Adaptive Finite Time Control of Nonlinear Systems Under Time-Varying Actuator Failures

This paper proposes a new finite-time tracking control strategy for a nonlinear uncertain system with actuation failures. The presented control scheme is not dependent on the exact model of system and actuation failures. By employing the approximation ability of fuzzy logic systems, an integrated adaptive controller is constructed, which accommodates for both system uncertainties and unknown actuator failures. Unlike the existing fault-tolerant control studies for actuator failures which can guarantee the system performances only if time tends to infinity, the presented control scheme can assure the system performances in finite time. By applying the Bhat and Bernstein theorem, the finite-time stability of system is proved. At last, the usefulness of the developed control scheme is illustrated by two examples.

Tracking Control of Hypersonic Vehicles with Input Saturation Based on Fast Terminal Sliding Mode

In this paper, the track problem of hypersonic vehicle is studied and analyzed with external disturbances, parameter uncertainty and input saturation. First, to make the design of controller convenient, the input and output linearized high-order model of hypersonic vehicle is transformed into a multi-variable second-order system model by introducing auxiliary error variables. To ensure the sliding mode manifold is practical finite time stable, an adaptive fast nonsingular terminal sliding mode controller is designed for hypersonic vehicle with unknown upper bound of disturbance. An adaptive anti-saturation fast nonsingular terminal sliding mode controller is designed by introducing hyperbolic tangent function an auxiliary system, which further solves the input saturation problem. Not only the requirement for actuator physical restraint is satisfied, but also the finite time stability of system sliding mode manifold is guaranteed at the same time. The vigorous proof is given using Lyapunov theory for the designed controllers. The numerical simulations are also conducted with the longitudinal nonlinear dynamic mode of hypersonic vehicle. The results demonstrate the effectiveness of the two designed controllers.

Adaptive Finite-Time Control of Nonlinear Quantized Systems With Actuator Dead-Zone

This paper investigates a finite-time control problem of nonlinear quantized systems with actuator dead-zone in a non-strict feedback form. By combining a simplified dead-zone model and the sector-bound characteristic of a hysteretic quantizer, the control difficulties caused by the coexistence of unknown actuator dead-zone and control signal quantization effect are overcome. By applying the approximation ability of neural network systems, an novel neural adaptive controller is constructed, which can compensate the unknown control gain. The designed neural controller can ensure the transient performance of nonlinear quantized systems with actuator dead-zone in finite-time. Based on the Bhat and Bernstein theorem, the finite-time stability of system is proved. Finally, a numerical example is given to verify the validity of the proposed approach.

Finite Time Stability Analysis of Switched Systems with Stable and Unstable Subsystems

ABSTRACTIn this paper, we study the finite time stability of nonlinear switched systems consisting of both stable and unstable subsystems. First, the finite time stability of systems is studied using the activation time of the subsystems. We show that if the total activation time of unstable subsystems is relatively small compared with that of finite time stable subsystems, then finite time stability of switched systems is guaranteed. Second, the finite time stability of systems is studied based on the comparison principle. We show that if the comparison system is finite time stable, then the finite time stability of switched systems is guaranteed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed methods.

Finite-time stabilization of linear systems via impulsive control

This paper introduces a new concept of finite-time stability of linear time-invariant impulsive systems. The sufficient condition of finite-time stability of the system via impulsive control at fixed times and variable times is obtained, respectively. Such sufficient conditions of finite-time stabilization are given in terms of matrix inequalities. A numerical example is presented to illustrate the efficiency of the proposed results.