Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach

In this paper, the problem of exponential stability in mean square for stochastic systems with multiple delays is investigated. A delay-dependent sufficient condition is derived in terms of linear matrix inequalities (LMIs) by using a descriptor model transformation of the system and by applying Moon's inequality for bounding cross terms. The criteria obtained in this paper can be tested numerically very efficiently using interior point algorithms. An example shows that the proposed methods are less conservative than the other methods.

[1]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[2]  Silviu-Iulian Niculescu,et al.  On delay-dependent stability under model transformations of some neutral linear systems , 2001 .

[3]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[4]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[5]  X. Mao,et al.  Robustness of exponential stability of stochastic differential delay equations , 1996, IEEE Trans. Autom. Control..

[6]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[7]  Ju-H. Park.  A new delay-dependent criterion for neural systems with multiple delays , 2001 .

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  D. Yue,et al.  Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties , 2001 .

[10]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[11]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[12]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[13]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..