| | |
Summary: CONTINUOUS AND DISCRETE TIME SPR DESIGN
USING FEEDBACK
C. Abdallah, P. Dorato, and S. Karni
EECE Department
University of New Mexico
Albuquerque, NM 87131, USA
March 9, 1997
ABSTRACT
This paper presents necessary and suÆcient conditions for the existence of a feedback
compensator that will render a given continuous-time or discrete-time linear system
SPR. When these conditions hold, the controller is explicitely found.
1 INTRODUCTION
The concepts of Positive-Real (PR) and Strictly-Positive-Real (SPR) functions and
matrices have been very useful in network theory [1], adaptive control [2] and ro-
bust control [3]. These concepts have also been generalized to include discrete-time
systems [4] and [5]. The importance of PR and SPR matrices is obvious when
dealing with uncertain systems. In this situation, a nominal SPR transfer function
allows for large passive uncertainties without the loss of stability [2] and [5]. The
standard de nition of SPR matrices [6], here termed strong SPR, is usually diÆ-
cult to apply. Moreover, it was recently shown [7] that the strong SPR de nition
|
