On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

[1]  C. Wen,et al.  Switched and Impulsive Systems: Analysis, Design, and Applications , 2005, IEEE Transactions on Automatic Control.

[2]  M. De la Sen,et al.  The generalized Beverton–Holt equation and the control of populations , 2008 .

[3]  Manuel de la Sen.  Stability criteria for linear time-invariant systems with point delays based on one-dimensional Routh-Hurwitz tests , 2007, Appl. Math. Comput..

[4]  Hak-Keung Lam,et al.  Stability analysis of discrete-time fuzzy-model-based control systems with time delay: Time delay-independent approach , 2008, Fuzzy Sets Syst..

[5]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[6]  Lansun Chen,et al.  Research Article Stage-Structured Impulsive SI Model for Pest Management , 2007 .

[7]  M. De la Sen,et al.  A note on the stability of linear time-delay systems with impulsive inputs , 2003 .

[8]  M. Sen.  Robust stability analysis and dynamic gain-scheduled controller design for point time-delay systems with parametrical uncertainties , 2008 .

[9]  Helong Liu,et al.  Stability results on age-structured SIS epidemic model with coupling impulsive effect , 2006 .

[10]  Lansun Chen,et al.  On a periodic time-dependent model of population dynamics with stage structure and impulsive effects. , 2008 .

[11]  Wang Zheqing,et al.  Numerical Stability Test of Neutral Delay Differential Equations , 2008 .

[12]  Baotong Cui,et al.  Existence and global attractivity of almost periodic solutions for neural field with time delay , 2008, Appl. Math. Comput..

[13]  Manuel de la Sen.  Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays , 2007, Appl. Math. Comput..

[14]  M. De la Sen,et al.  On the stability properties of linear dynamic time-varying unforced systems involving switches between parameterizations from topologic considerations via graph theory , 2007, Discret. Appl. Math..

[15]  M. De la Sen,et al.  Model-Matching-Based Control of the Beverton-Holt Equation in Ecology , 2008 .

[16]  A. U. Afuwape,et al.  Stability and boundedness of solutions of a kind of third-order delay differential equations , 2010 .

[17]  M. De la Sen,et al.  About the Properties of a Modified Generalized Beverton-Holt Equation in Ecology Models , 2008 .

[18]  Alakes Maiti,et al.  Effect of time-delay on a food chain model , 2008, Appl. Math. Comput..

[19]  Manuel de la Sen,et al.  A Control Theory point of view on Beverton-Holt equation in population dynamics and some of its generalizations , 2008, Appl. Math. Comput..

[20]  Weidong Zhang,et al.  Sliding Mode Control of Uncertain Neutral Stochastic Systems with Multiple Delays , 2008 .

[21]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[22]  Huaguang Zhang,et al.  Robust exponential stability analysis of neural networks with multiple time delays , 2007, Neurocomputing.

[23]  M. De la Sen,et al.  The environment carrying capacity is not independent of the intrinsic growth rate for subcritical spawning stock biomass in the Beverton–Holt equation , 2007 .

[24]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[25]  Ju H. Park,et al.  On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays , 2008, Appl. Math. Comput..

[27]  Asier Ibeas,et al.  Robustly Stable Adaptive Control of a Tandem of Master–Slave Robotic Manipulators With Force Reflection by Using a Multiestimation Scheme , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[29]  On the Study of Chemostat Model with Pulsed Input in a Polluted Environment , 2007 .

[30]  Yong-Hong Fan,et al.  Permanence for a Discrete Model with Feedback Control and Delay , 2008 .

[31]  M. De la Sen,et al.  On the uniform exponential stability of a wide class of linear time-delay systems , 2004 .

[32]  M. Sen.  On Minimal Realizations and Minimal Partial Realizations of Linear Time-Invariant Systems Subject to Point Incommensurate Delays , 2008 .

[33]  Qiong Liu.  Almost Periodic Solution of a Diffusive Mixed System with Time Delay and Type III Functional Response , 2008 .

[34]  Chunjin Wei,et al.  A Delayed Epidemic Model with Pulse Vaccination , 2008 .

[35]  Wang Qi,et al.  Almost periodic solution for n-species Lotka-Volterra competitive system with delay and feedback controls , 2008, Appl. Math. Comput..