New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

[1]  F. Amato,et al.  Finite-time stability of discrete-time systems , 2004, Proceedings of the 2004 American Control Conference.

[2]  Wei Xing Zheng,et al.  Finite-time stabilization for a class of switched time-delay systems under asynchronous switching , 2013, Appl. Math. Comput..

[3]  Yijing Wang,et al.  New criterion for finite-time stability of linear discrete-time systems with time-varying delay , 2013, J. Frankl. Inst..

[4]  Yanjun Shen,et al.  Finite-time control of discrete-time systems with time-varying exogenous disturbance , 2009 .

[5]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[6]  Jirapong Puangmalai,et al.  An Improved Finite-Time Stability and Stabilization of Linear System with Constant Delay , 2014 .

[7]  D. Debeljkovic,et al.  Finite-time stability of delayed systems , 2000 .

[8]  E. Moulay,et al.  Finite time stability and stabilization of a class of continuous systems , 2006 .

[9]  K. Mukdasai,et al.  New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays , 2013 .

[10]  Yanjun Shen Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance , 2008 .

[12]  Sreten B. Stojanovic,et al.  Robust Finite-Time Stability and Stabilization of Linear Uncertain Time-Delay Systems , 2013 .

[13]  Pin-Lin Liu,et al.  Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays. , 2013, ISA transactions.

[14]  Francesco Amato,et al.  Input to Output Finite-Time Stabilization of Discrete-Time Linear Systems , 2011 .

[15]  Fuad E. Alsaadi,et al.  New results on robust finite-time boundedness of uncertain switched neural networks with time-varying delays , 2015, Neurocomputing.

[16]  Jun Cheng,et al.  Finite-time boundedness of state estimation for neural networks with time-varying delays , 2014, Neurocomputing.

[17]  Hamid Reza Karimi,et al.  Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay , 2014, J. Frankl. Inst..

[18]  Zheng Yuan,et al.  Finite-time Control Synthesis of Networked Control Systems with Time-varying Delays , 2011 .

[19]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

[20]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[21]  D. Debeljkovi,et al.  FINITE-TIME STABILITY AND STABILIZATION OF LINEAR TIME-DELAY SYSTEMS , 2012 .

[22]  Sreten B. Stojanovic,et al.  Finite-time stability of discrete-time systems with time-varying delay , 2012 .

[23]  N. I. Morozov,et al.  Stability of motion over a finite interval of time , 1978 .

[24]  Tianjian Yu,et al.  Finite-Time Stabilization of Uncertain Switched Positive Linear Systems with Time-Varying Delays , 2015 .