Stability Analysis of Time-Varying Neutral Time-Delay Systems

We propose a new technique of stability analysis for a general family of linear time-varying systems with delay of neutral type. We establish results of exponential stability through a new technique which relies on the notion of nonnegative system and the design of linear time-varying Lyapunov functionals. However, the studied systems are not assumed to be nonnegative.

[1]  Alfredo Germani,et al.  Internally Positive Representation of a Class of Continuous Time Systems , 2012, IEEE Transactions on Automatic Control.

[2]  V. Kolmanovskii,et al.  Stability of nonlinear differential equations with distributed , 1998 .

[3]  Olivier Bernard,et al.  Asymptotically Stable Interval Observers for Planar Systems With Complex Poles , 2010, IEEE Transactions on Automatic Control.

[4]  Denis V. Efimov,et al.  Interval Observers for Time-Varying Discrete-Time Systems , 2013, IEEE Transactions on Automatic Control.

[5]  M. Krstić.  Delay Compensation for Nonlinear, Adaptive, and PDE Systems , 2009 .

[6]  Michael Malisoff,et al.  Review of Lyapunov Functions , 2009 .

[7]  Zhong-Ping Jiang,et al.  Stability results for systems described by coupled retarded functional differential equations and functional difference equations , 2009 .

[8]  Wassim M. Haddad,et al.  Stability theory for nonnegative and compartmental dynamical systems with time delay , 2004, Proceedings of the 2004 American Control Conference.

[9]  Jonathan R. Partington,et al.  Stability of Neutral Systems with Commensurate Delays and Poles Asymptotic to the Imaginary Axis , 2011, SIAM J. Control. Optim..

[10]  J. Richard,et al.  Stability, attraction domains, and ultimate boundedness for nonlinear neutral systems , 1998 .

[11]  M. Malisoff,et al.  Constructions of Strict Lyapunov Functions , 2009 .

[12]  A Alejandro Alvarez Aguirre,et al.  Remote control and motion coordination of mobile robots , 2011 .

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

[14]  Pham Huu Anh Ngoc.  Stability of Positive Differential Systems With Delay , 2013, IEEE Transactions on Automatic Control.

[15]  Miroslav Krstic,et al.  Lyapunov-Krasovskii functionals and application to input delay compensation for linear time-invariant systems , 2012, Autom..

[16]  Frédéric Mazenc,et al.  Interval observers for discrete-time systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[17]  Wilfrid Perruquetti,et al.  On reduced-order interval observers for time-delay systems , 2013, 2013 European Control Conference (ECC).

[18]  Wassim M. Haddad,et al.  Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay , 2004 .

[19]  Alfredo Germani,et al.  Representation of a Class of MIMO Systems via Internally Positive Realization , 2010, Eur. J. Control.

[20]  W. Haddad,et al.  Nonnegative and Compartmental Dynamical Systems , 2010 .

[21]  Zhong-Ping Jiang,et al.  On the Liapunov-Krasovskii methodology for the ISS of systems described by coupled delay differential and difference equations , 2008, Autom..

[22]  Michael Malisoff,et al.  Stabilization of linear time varying systems with input delays: Application to rapidly time varying systems , 2013, 52nd IEEE Conference on Decision and Control.

[23]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..

[24]  Jack K. Hale,et al.  Functional differential equations: Basic theory , 1993 .

[25]  Alfredo Germani,et al.  A New Approach to the Internally Positive Representation of Linear MIMO Systems , 2012, IEEE Transactions on Automatic Control.