Aizerman's problem for nonlinear discrete-time control systems

Abstract

Sufficient conditions for input–output stability of a class of nonlinear discrete-time systems are derived. It is proved that systems having positive Green functions (impulse response) satisfy the Aizerman's conjecture in the input–output version. The stability criteria are formulated in terms of the stable polynomials. Besides, we offer some new positivity conditions for the Green functions. All conditions presented here are in terms of known quantities and therefore easily verified.

Keywords:

• nonlinear discrete-time systems
• input–output stability
• Aizerman's conjecture
• Green functions

AMS (MOS) Subject Classifications::

• 39A11

Acknowledgements

The author thanks Professor M.I. Gil' for his careful reading and insightful critiques of preliminary versions of this article.

Notes

This research was supported by Fondecyt Chile under Grant No. 1.070.980.