Operator-Type Stability Theorem for Retarded Stochastic Systems With Application

In this note, asymptotic stability of general retarded stochastic systems is investigated by virtue of the so called operator-type technique. The method for rewriting system models via functional difference operators is proposed, and the asymptotic stability theorem based on functional difference operators is established. The models and conditions considered are all in general forms, and the results obtained are suitable for neutral systems. As a theoretical application, the delayed feedback control of general time varying linear stochastic systems with distributed delay is investigated, two control strategies are designed and the corresponding stability criteria are established. The efficiency of the operator-type technique is illustrated by an example.

[1]  Hiroshi Ito,et al.  On Saturation, Discontinuities, and Delays, in iISS and ISS Feedback Control Redesign , 2012, IEEE Transactions on Automatic Control.

[2]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[3]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[4]  Pierdomenico Pepe,et al.  Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability , 2008, IEEE Transactions on Automatic Control.

[5]  Pierre-Alexandre Bliman,et al.  Lyapunov equation for the stability of linear delay systems of retarded and neutral type , 2002, IEEE Trans. Autom. Control..

[6]  T. A. Burton,et al.  Stability theorems for nonautonomous functional-differential equations by Liapunov functionals , 1989 .

[7]  Iasson Karafyllis.  Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations , 2005, CDC 2005.

[8]  Yun Zhang,et al.  Razumikhin-Type Theorems on $p$th Moment Exponential Stability of Impulsive Stochastic Delay Differential Equations , 2010, IEEE Transactions on Automatic Control.

[9]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[10]  Bing Li,et al.  Mean square asymptotic behavior of stochastic neural networks with infinitely distributed delays , 2009, Neurocomputing.

[11]  A. E. Pearson,et al.  A multistage reduction technique for feedback stabilizing distributed time-lag systems , 1987, Autom..

[12]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[13]  Zhi-Hong Guan,et al.  Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach , 2005, Syst. Control. Lett..

[14]  Peng Shi,et al.  Robust Stochastic Stabilization and H∞ Control for Neutral Stochastic Systems with Distributed Delays , 2011, Circuits Syst. Signal Process..

[15]  XUEYAN ZHAO,et al.  New Type of Stability Criteria for Stochastic Functional Differential Equations via Lyapunov Functions , 2014, SIAM J. Control. Optim..

[16]  James Lam,et al.  Robust Stability for Interval Stochastic Neural Networks with Time-Varying Discrete and Distributed Delays , 2011 .

[17]  Chengming Huang,et al.  Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay , 2009, Autom..

[18]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .