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Unformatted text preview: k = n-1, C k Π k x = C k x-C k C * k C k C * k C k x = 0, and Π k x-x = C k x C k C * k C * k ∈ R ( C * k ) = ⇒ (Π k x-x ) ⊥ N ( C k ), so Π k projects orthogonally into the nullspace of C k . Therefore ˆ a k = Π k (ˆ a k-1-a k ) + a k is the desired estimate. Exercise 3. Note that Φ( t,τ ) is always invertible. To steer the system from x to y on [ τ ,t ] ⊃ [ τ,t ], choose an input that steers the system from Φ( τ,τ ) x to Φ( t ,t )-1 y on [ τ,t ]. As a counterexample when [ τ ,t ] ⊂ ( τ,t ), consider a controllable system for which B ( σ ) ≡ for σ ∈ [ τ ,t ]....
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This note was uploaded on 04/11/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
- Fall '10