Abstract
Given a contractive linear system T which is represented as a causal linear contractive operator on a Hilbert space H, we study the question: When does there exist an isometric or unitary causal extension of T to H ⊕H? Here causality is formulated as a lower triangularity condition and we assume the same causality structure for the extension. This question is often referred to as the generalized Darlington synthesis problem for linear time-varying systems.
Original language | English |
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Pages (from-to) | 26-43 |
Number of pages | 18 |
Journal | Mathematics of Control, Signals, and Systems |
Volume | 16 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2003 |
Keywords
- Causal linear systems
- Darlington synthesis
- Isometric dilations
- Nest algebras
- Time-varying linear
- Unitary dilations
ASJC Scopus subject areas
- Control and Systems Engineering
- Signal Processing
- Control and Optimization
- Applied Mathematics