online read us now
Paper details
Number 2 - June 2003
Volume 13 - 2003
Quantitative Lp stability analysis of a class of linear time-varying feedback systems
Pini Gurfil
Abstract
The Lp stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for Lp stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.
Keywords
Lpstability, time-varying Lur'e systems, functional analysis