Stability of continuous-time systems with stochastic delay

The stability of linear continuous-time systems with stochastic delay is investigated in this paper. The delay is assumed to be a piece-wise constant function of time such that it switches between finitely many different values stochastically. The stability of the stochastic system is assessed in terms of the convergence of the second moment of the state. Using infinite-dimensional solution operators, a stochastic linear map is constructed, allowing us to derive necessary and sufficient conditions of second moment stability. The discretization of the solution operators can be used to draw stability charts. An illustrative example is discussed to shed some light on the effects of stochastic delays on stability.

[1]  Dimitri Breda,et al.  Solution operator approximations for characteristic roots of delay differential equations , 2006 .

[2]  Fan Bai,et al.  Reliability Analysis of DSRC Wireless Communication for Vehicle Safety Applications , 2006, 2006 IEEE Intelligent Transportation Systems Conference.

[3]  G. Orosz,et al.  ON THE STABILITY OF CONTINUOUS-TIME SYSTEMS WITH STOCHASTIC DELAY: APPLICATIONS TO GENE REGULATORY CIRCUITS , 2014 .

[4]  R. Ryan.  Introduction to Tensor Products of Banach Spaces , 2002 .

[5]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[6]  Shiyin Qin,et al.  Stability analysis and controller design for networked control systems with random time delay , 2009, 2009 9th International Conference on Electronic Measurement & Instruments.

[7]  U. Ozguner,et al.  Stability of Linear Feedback Systems with Random Communication Delays , 1991, 1991 American Control Conference.

[8]  LieJune Shiau,et al.  Stochastic Delay Accelerates Signaling in Gene Networks , 2011, PLoS Comput. Biol..

[9]  A. Arkin,et al.  It's a noisy business! Genetic regulation at the nanomolar scale. , 1999, Trends in genetics : TIG.

[10]  K. Maciej Przyłuski.  Stability of linear infinite-dimensional systems revisited , 1988 .

[11]  Julian Lewis.  Autoinhibition with Transcriptional Delay A Simple Mechanism for the Zebrafish Somitogenesis Oscillator , 2003, Current Biology.

[12]  Gábor Stépán,et al.  Semi-Discretization for Time-Delay Systems: Stability and Engineering Applications , 2011 .

[13]  Wim Michiels,et al.  Stability analysis of systems with stochastically varying delays , 2009, Syst. Control. Lett..

[14]  I. V. Kolmanovsky,et al.  Stochastic stability of a class of nonlinear systems with randomly varying time-delay , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[15]  Vladimir L. Kharitonov,et al.  On the stability of linear systems with uncertain delay , 2003, IEEE Trans. Autom. Control..

[16]  Gábor Orosz,et al.  Exact stability analysis of discrete-time linear systems with stochastic delays , 2014, 2014 American Control Conference.

[17]  Gábor Orosz,et al.  Stability and Frequency Response Under Stochastic Communication Delays With Applications to Connected Cruise Control Design , 2017, IEEE Transactions on Intelligent Transportation Systems.