State Maps from Integration by Parts
van der Schaft, Arjan and Rapisarda, Paolo (2011) State Maps from Integration by Parts. SIAM Journal on Control and Optimization, 49, (6), 2415-2439.
We develop a new approach to the construction of state vectors for linear time-invariant systems described by higher-order differential equations. The basic observation is that the concatenation of two solutions of higher-order differential equations results in another (weak) solution once their remainder terms resulting from (repeated) integration by parts match. These remainder terms can be computed in a simple and efficient manner by making use of the calculus of bilinear differential forms and two-variable polynomial matrices. Factorization of the resulting two-variable polynomial matrix defines a state map, as well as a state map for the adjoint system. Minimality of these state maps is characterized. The theory is applied to three classes of systems with additional structure, namely self-adjoint Hamiltonian, conservative port-Hamiltonian, and time-reversible systems. For the first two classes it is shown how the factorization leading to a (minimal) state map is equivalent to the factorization of another two-variable polynomial matrix, which is immediately derived from the external system characterization, and defines a symplectic, respectively, symmetric, bilinear form on the minimal state space.
|Keywords:||adjoint systems, Hamiltonian systems, state, integration by parts, factorization|
|Divisions:||Faculty of Physical and Applied Science > Electronics and Computer Science > Comms, Signal Processing & Control
|Date Deposited:||17 Nov 2011 17:32|
|Last Modified:||25 Aug 2012 02:57|
|Contributors:||van der Schaft, Arjan (Author)
Rapisarda, Paolo (Author)
|Further Information:||Google Scholar|
|ISI Citation Count:||1|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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