ece604 lecture 20

ece604 lecture 20 - Dec. 1, 2009 Linear Systems © Douglas...

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Unformatted text preview: Dec. 1, 2009 Linear Systems © Douglas Looze 1 Lecture 20 ECE 604 Linear Systems Doug Looze Dec. 1, 2009 Linear Systems © Douglas Looze 2 Announcements Problem set 6 due Reading – Bay, Chapter 7.1 Dec. 1, 2009 Linear Systems © Douglas Looze 3 Last Time Minimal realization – Controllable realization • Transform to canonical form • Minimal uses (C) and (O) states – From Hankel matrices • Markov parameters • Algorithm • Can use SVD Dec. 1, 2009 Linear Systems © Douglas Looze 4 Internal Stability – The unforced linear state equation is uniformly stable (S) if for every ε > 0 there exists δ > 0 such that if ( 29 t t t ε ≤ 2200 ≥ x δ < x then – The unforced linear state equation is uniformly exponentially stable (ES) if there exists γ > 0 and λ > 0 such that for any t and x ( 29 ( 29 t t t e t t λ γ-- ≤ 2200 ≥ x x Dec. 1, 2009 Linear Systems © Douglas Looze 5 Relationship to transition matrix Lyapunov transformations – Preserve internal stability...
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ece604 lecture 20 - Dec. 1, 2009 Linear Systems © Douglas...

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