Lossless and Dissipative Distributed Systems
- 1 January 2002
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 40 (5) , 1406-1430
- https://doi.org/10.1137/s0363012900368028
Abstract
This paper deals with linear shift-invariant distributed systems. By this we mean systems described by constant coefficient linear partial differential equations. e de ne dissipativity with respect to a quadratic differential form, i.e., a quadratic functional in the system variables and their partial derivatives. The main result states the equivalence of dissipativity and the existence of a storage function or a dissipation rate. The proof of this result involves the construction of the dissipation rate. e show that this problem can be reduced to Hilbert's 17th problem on the representation of a nonnegative rational function as a sum of squares of rational functionsKeywords
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