Rao, Shodhan and Rapisarda, Paolo
Autonomous linear lossless systems.
At 17th IFAC World Congress , Seoul, South Korea,
06 - 11 Jul 2008.
We define a lossless autonomous system as one having a quadratic differential form associated with it called an energy function, which is positive and which is conserved. We define an oscillatory system as one which has all its trajectories bounded on the entire time axis. In this paper, we show that an autonomous system is lossless if and only if it is oscillatory. Next we discuss a few properties of energy functions of autonomous lossless systems and a suitable way of splitting a given energy function into its kinetic and potential energy components.
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