Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

Abstract The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

[1]  Derong Liu,et al.  Asymptotic Stability of a Class of Linear Discrete Systems with Multiple Independent Variables , 2003 .

[2]  Tatsushi Ooba,et al.  Stability of linear discrete dynamics employing state saturation arithmetic , 2003, IEEE Trans. Autom. Control..

[3]  Vimal Singh,et al.  Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: an LMI approach , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[4]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[5]  Ralph R. Martin,et al.  Delay-dependent robust stabilisation of discrete-time systems with time-varying delay , 2006 .

[6]  Vimal Singh.  Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic , 2007 .

[7]  Pedro Luis Dias Peres,et al.  Robust 𝒽∞ filtering for uncertain discrete-time state-delayed systems , 2001, IEEE Trans. Signal Process..

[8]  A. Michel,et al.  Dynamical systems with saturation nonlinearities , 1994 .

[9]  V. Krishna Rao Kandanvli,et al.  Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities , 2008 .

[10]  V. Singh,et al.  Stability analysis of discrete-time systems in a state-space realisation with state saturation nonlinearities: linear matrix inequality approach , 2005 .

[11]  R. Roberts,et al.  Digital filter realizations without overflow oscillations , 1978 .

[12]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[13]  Huijun Gao,et al.  Induced l/sub 2/ and generalized H/sub 2/ filtering for systems with repeated scalar nonlinearities , 2005, IEEE Transactions on Signal Processing.

[14]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[15]  A. Michel,et al.  Stability analysis of state-space realizations for two-dimensional filters with overflow nonlinearities , 1994 .

[16]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

[17]  Haranath Kar.  An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic , 2007, Digit. Signal Process..

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

[19]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[20]  Vimal Singh.  Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic: An LMI approach , 2006, Digit. Signal Process..

[21]  Yun-Chung Chu,et al.  Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities , 1999, IEEE Trans. Autom. Control..

[22]  V. Singh,et al.  Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities , 2001, IEEE Trans. Signal Process..

[23]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[24]  Vimal Singh,et al.  Stability analysis of discrete-time systems in a state-space realisation with partial state saturation nonlinearities , 2003 .

[25]  A. Michel,et al.  Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters , 1992 .