New delay-dependent stability result and its application to robust performance analysis for discrete-time systems with delay

The problem of delay-dependent stability analysis for discrete-time systems with time-varying delay is addressed in this paper. By introducing a novel Lyapunov functional and a couple of slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequality. Via the proposed method, delay-dependent results on robust performance analysis for discrete time-delay systems are also presented. Numerical examples are provided to show the reduced conservatism than the existing results.

[1]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers , 2004, Syst. Control. Lett..

[2]  Ching-Min Lee,et al.  A New Finite Sum Inequality Approach to Delay Dependent Control For Discrete Singular Systems , 2012 .

[3]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[4]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

[5]  D. Yue,et al.  A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay , 2009 .

[6]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[7]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[8]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[9]  Shengyuan Xu,et al.  H∞ and positive-real control for linear neutral delay systems , 2001, IEEE Trans. Autom. Control..

[10]  Emilia Fridman,et al.  Delay-Dependent H∞ Control of Uncertain Discrete Delay Systems , 2005, Eur. J. Control.

[11]  Naser F. Al-Muthairi,et al.  Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties , 1994, IEEE Trans. Autom. Control..

[12]  Hongyong Yang,et al.  Further Results Concerning Delay-Dependent Control for Uncertain Discrete-Time Systems with Time-Varying Delay , 2009 .

[13]  U. Shaked,et al.  Stability and guaranteed cost control of uncertain discrete delay systems , 2005 .

[14]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[15]  Xiefu Jiang,et al.  Stability criteria for linear discrete-time systems with interval-like time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Huijun Gao,et al.  Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay , 2004 .

[17]  Shengyuan Xu,et al.  Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems , 2005 .

[18]  W. Kwon,et al.  Delay-dependent robust stabilization of uncertain discrete-time state-delayed systems , 2002 .

[19]  Shengyuan Xu,et al.  Improved stability criterion and its applications in delayed controller design for discrete-time systems , 2008, Autom..

[20]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[21]  E. Fridman,et al.  Robust Filtering of Linear Systems With Time-Varying Delay , 2003 .

[22]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.