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Relationships Between Positive Real, Passive Dissipative, & Positive Systems Nicholas Kottenstette and Panos J. Antsaklis
 

Summary: Relationships Between Positive Real, Passive Dissipative, & Positive Systems
Nicholas Kottenstette and Panos J. Antsaklis
Institute for Software Integrated Systems, Vanderbilt University, Email: nkottens@isis.vanderbilt.edu
Department of Electrical Engineering, University of Notre Dame, Email: antsaklis.1@nd.edu
Abstract-- This paper shows how: i) (strongly) positive real;
ii) (asymptotically stable) dissipative (strictly-input) passive;
and iii) (Lm
2 -stable strictly) positive; continuous time system def-
initions are equivalent for linear time invariant (LTI) systems.
In parallel this paper shows how: i) (strictly) positive real; ii)
(asymptotically stable) dissipative (strictly-input) passive; and
iii) (lm
2 -stable strictly) positive; discrete time system definitions
are equivalent for LTI systems. A frequency test is derived to
determine if a single input single output LTI system is strictly
output passive. Finally, the necessary conditions to synthesize
a system which is both passive and stable but neither strictly-
input passive nor strictly-output passive are presented.
I. INTRODUCTION
In our recent research we have pursued constructive

  

Source: Antsaklis, Panos - Department of Electrical Engineering, University of Notre Dame

 

Collections: Engineering