Decay rate constrained stability analysis for positive systems with discrete and distributed delays

This paper is concerned with the decay rate constrained exponential stability analysis for continuous-time positive systems with both time-varying discrete and distributed delays. A necessary and sufficient condition is first given to ensure that a positive system with distributed delay is exponentially stable and satisfies a prescribed decay rate. Furthermore, by exploiting the monotonicity of the trajectory of a constant delay system and comparing the trajectory of the time-varying delay system with that of the constant delay system, the results are extended to positive systems with both bounded time-varying discrete delays and distributed delays.

[1]  Chenghui Zhang,et al.  Exponential stability analysis for positive systems with delays , 2011, Proceedings of the 30th Chinese Control Conference.

[2]  Mustapha Ait Rami,et al.  Solvability of static output-feedback stabilization for LTI positive systems , 2011, Syst. Control. Lett..

[3]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[4]  Tadeusz Kaczorek,et al.  Positive Linear Systems Consisting of $n$ Subsystems With Different Fractional Orders , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  James Lam,et al.  $H_{\infty}$ Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach , 2010, IEEE Transactions on Automatic Control.

[6]  James Lam,et al.  L∞-gain analysis for positive systems with distributed delays , 2014, Autom..

[7]  F. Tadeo,et al.  Controller Synthesis for Positive Linear Systems With Bounded Controls , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[9]  Min Meng,et al.  Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization , 2013, J. Frankl. Inst..

[10]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

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

[12]  J. Jacquez.  Compartmental analysis in biology and medicine , 1985 .

[13]  Jon Rigelsford,et al.  Positive 1D and 2D Systems , 2002 .

[14]  M. Lewin.  On nonnegative matrices , 1971 .

[15]  Xingwen Liu,et al.  Constrained Control of Positive Systems with Delays , 2009, IEEE Transactions on Automatic Control.

[16]  Chuangyin Dang,et al.  Stability Analysis of Positive Switched Linear Systems With Delays , 2011, IEEE Transactions on Automatic Control.

[17]  Xudong Zhao,et al.  Stability of a class of switched positive linear time‐delay systems , 2013 .

[18]  Tadeusz Kaczorek,et al.  Fractional Positive Continuous-Time Linear Systems and Their Reachability , 2008, Int. J. Appl. Math. Comput. Sci..

[19]  Long Wang,et al.  Stability Analysis of Positive Systems With Bounded Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[21]  Long Wang,et al.  Stability Analysis for Continuous-Time Positive Systems With Time-Varying Delays , 2010, IEEE Transactions on Automatic Control.

[22]  Peng Shi,et al.  Stability of switched positive linear systems with average dwell time switching , 2012, Autom..

[23]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[24]  Diego Napp Avelli,et al.  Characterization and Stability of Autonomous Positive Descriptor Systems , 2012, IEEE Transactions on Automatic Control.

[25]  James Lam,et al.  On ℓ∞ and L∞ gains for positive systems with bounded time-varying delays , 2015, Int. J. Syst. Sci..

[26]  J. Lam,et al.  Decay rate constrained stabilization of positive systems using static output feedback , 2011 .

[27]  H. Caswell.  Matrix population models : construction, analysis, and interpretation , 2001 .