Name
Abstract | ||
|---|---|---|
This paper deals with linear shift-invariant distributed systems. By this we mean systems described by constant coefficient linear partial differential equations. We define 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. We 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 functions. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0363012900368028 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
behavioral theory,paper deal,dissipation rate,storage functions,nonnegative rational function,storage function,linear multidimensional systems,lossless systems,quadratic differential forms,positivity,partial derivative,main result,dissipativeness,coefficient linear partial differential,quadratic differential form,rational function,polynomial matrices,linear shift-invariant,distributed system,partial differential equation,multidimensional system,sum of squares | Mathematical optimization,Mathematical analysis,Dissipation,Constant coefficients,Dissipative system,Partial derivative,Quadratic differential,Explained sum of squares,Rational function,Mathematics,Distributed computing,Spectral theorem | Journal |
Volume | Issue | ISSN |
40 | 5 | 0363-0129 |
Citations | PageRank | References |
22 | 6.10 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Harish K. Pillai | 1 | 90 | 20.79 |
| Jan C. Willems | 2 | 427 | 112.68 |