ISS Criterion for the Realization of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Interference
- 6 Downloads
This paper investigates the problem of the input-to-state stability (ISS) of fixed-point state-space digital filters in the presence of saturation overflow arithmetic and external interference. By utilizing an augmented Lyapunov function and the passivity property associated with multiple saturation nonlinearities, a new criterion for the ISS of interfered digital filters with saturation is proposed. When the external interference is present, the criterion can be used to determine ISS of digital filters. Without the external interference, the criterion is capable of detecting the asymptotic stability of digital filters. The proposed ISS criterion is in linear matrix inequality framework and, hence, is computationally tractable. The obtained criterion turns out to be less conservative than a recently reported ISS criterion. The superiority of the presented approach over the existing techniques is confirmed by numerical examples.
KeywordsDigital filter External interference Finite wordlength effect Input-to-state stability Saturation arithmetic
The authors thank the Editors and the anonymous reviewers for their constructive comments and suggestions to improve the manuscript.
- 11.J. Löfberg, YALMIP: a toolbox for modeling and optimization in MATLAB, in Proceedings of the 2004 IEEE International Symposium on CACSD, Taipei, Taiwan, 2004, pp. 284–289Google Scholar
- 13.J. Monteiro, R.V. Leuken (eds.), Integrated Circuit and System Design: Power and Timing Modeling, Optimization and Simulation (Springer, Berlin, 2010)Google Scholar
- 15.J.G. Proakis, D.G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications (Pearson Prentice Hall, New Jersey, 1996)Google Scholar
- 16.L.R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, New Jersey, 1975)Google Scholar