Robust finite-time output feedback control of perturbed double integrator

We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

This paper investigates the problem of finite-time state feedback stabilization for nonholonomic mobile robot with stochastic disturbance in the forward velocity. First of all, an appropriate state/input transformation is introduced to convert the mentioned control model into stochastic nonholonomic system in chain form. Then, by using stochastic finite-time stability theorem and the method of adding a power integrator, a state feedback controller is obtained. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the closed-loop system is globally finite-time regulated at origin in probability. A simulation example is finally provided to demonstrate the validness of the proposed approach.

Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay

Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales

This study is concerned with robust finite-time stability and stabilisation of a class of switched positive systems. By using the multiple linear copositive Lyapunov function approach, sufficient conditions of finite-time stability and finite-time boundedness are constructed, respectively. l 1-gain is used to analyse the disturbance attenuation performance of the systems, and a finite-time weighted l 1-gain is obtained under bounded exogenous disturbances. Then, the problem of robust finite-time stabilisation of non-autonomous systems with a weighted l 1-gain is solved. All the proposed conditions are formulated in linear programming. Finally, two illustrative examples are given to show the validity of the theoretical results.

In this paper, the finite-time stability analysis and stabilization for switched discrete linear system are investigated. A sufficient condition for finite-time stability of switched system is given by searching for a set of positive matrices which is less conservative than searching for a single positive matrix. Then the static-state feedback and dynamic output feedback finite-time stabilization are proposed. Several examples are given to illustrate the results within this paper.

This technical note is concerned about the finite-time stability and stabilization for Ito stochastic systems with Markovian switching. A mode-dependent parameter approach is proposed to give a sufficient condition for finite-time stability, and its superiority to common parameter approach is analyzed. Moreover, the finite-time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities. A N-mode algorithm is given for solving the obtained matrix inequalities arising from finite-time stability(stabilization). Finally, an example is employed to illustrate the effectiveness of our obtained results.

ABSTRACTThis paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.

This paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basis for the stability proof of the system considered. The sliding mode control method is applied for robust control of uncertain variable fractional order systems; furthermore, the chattering phenomenon is avoided. And the finite time stability of the systems under control law is proved based on the proposed stability criterion. Finally, numerical simulations are proposed and the efficiency of the controller is verified.

Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method