On Finite-Time Stability of Linear Positive Differential-Algebraic Delay Equations

This brief addresses finite-time stability of linear positive differential-algebraic equations with delay. Being different from the Lyapunov function method, delay-dependent sufficient conditions for positivity and finite-time stability of the system are established in terms of standard linear programming problems. A numerical example is given to illustrate the obtained results.

[1]  Cédric Langbort,et al.  A linear programming approach to routing control in networks of constrained linear positive systems , 2012, Autom..

[2]  Hieu Minh Trinh,et al.  Design of Reduced-Order Positive Linear Functional Observers for Positive Time-Delay Systems , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Hieu Minh Trinh,et al.  Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities , 2017, IMA J. Math. Control. Inf..

[4]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[5]  Le Van Hien,et al.  An explicit criterion for finite-time stability of linear nonautonomous systems with delays , 2014, Appl. Math. Lett..

[6]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[7]  H. Trinh,et al.  Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays , 2017 .

[8]  Volker Mehrmann,et al.  Differential-Algebraic Equations: Analysis and Numerical Solution , 2006 .

[9]  Stephen L. Campbell,et al.  Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions , 2009, Appl. Math. Comput..

[10]  N. H. Muoi,et al.  Robust finite-time stability of linear differential-algebraic delay equations , 2015 .

[11]  Dimitri Peaucelle,et al.  LMI approach to linear positive system analysis and synthesis , 2014, Syst. Control. Lett..

[12]  Elena Virnik,et al.  Stability analysis of positive descriptor systems , 2008 .

[13]  Paolo Mercorelli,et al.  Global Finite-Time Stabilization of Planar Linear Systems With Actuator Saturation , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[15]  Andrey Polyakov,et al.  Interval observer design for estimation and control of time-delay descriptor systems , 2015, Eur. J. Control.

[16]  Zhengzhi Han,et al.  Robust finite-time stability and stabilisation of switched positive systems , 2014 .

[17]  Elena Virnik.  Analysis of Positive Descriptor Systems: Topics in Systems and Control Theory , 2008 .