Finite-time stability theorem of stochastic nonlinear systems

A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Ito differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper.

[1]  E. Moulay,et al.  Finite time stability and stabilization of a class of continuous systems , 2006 .

[2]  Wilfrid Perruquetti,et al.  Finite-time stability and stabilization of time-delay systems , 2008, Syst. Control. Lett..

[3]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[4]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[5]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems , 2005, IEEE Transactions on Automatic Control.

[6]  V. Haimo.  Finite time controllers , 1986 .

[7]  D. Debeljkovic,et al.  FINITE TIME STABILITY ANALYSIS OF LINEAR AUTONOMOUS FRACTIONAL ORDER SYSTEMS WITH DELAYED STATE , 2005 .

[8]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[9]  W. Haddad,et al.  Finite-time stabilization of nonlinear impulsive dynamical systems☆ , 2008 .

[10]  E. Ryan.  Finite-time stabilization of uncertain nonlinear planar systems , 1991 .

[11]  Wilfrid Perruquetti,et al.  Finite time stability conditions for non-autonomous continuous systems , 2008, Int. J. Control.

[12]  Ying-Xu Yang,et al.  Finite-time stability and stabilization of nonlinear stochastic hybrid systems☆ , 2009 .

[13]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[14]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[15]  G. Yin,et al.  Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach , 1997 .

[16]  A. Michel,et al.  Practical Stability and Finite-Time Stability of Discontinuous Systems , 1972 .

[17]  Sophie Tarbouriech,et al.  Finite-Time Stabilization of Linear Time-Varying Continuous Systems , 2009, IEEE Transactions on Automatic Control.

[18]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

[19]  Jevon M. Avis,et al.  Design of finite‐time stabilizing controllers for nonlinear dynamical systems , 2009 .

[20]  Gianmaria De Tommasi,et al.  Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems , 2009, IEEE Transactions on Automatic Control.

[21]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[22]  H. Kushner.  Finite time stochastic stability and the analysis of tracking systems , 1966 .

[23]  E. P. Ryan.  Singular optimal controls for second-order saturating systems , 1979 .

[24]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[25]  Wassim M. Haddad,et al.  Finite-Time Stabilization of Nonlinear Dynamical Systems via Control Vector Lyapunov Functions , 2007, 2007 American Control Conference.

[26]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..