This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A = A T and For all x we have x T Ax ≥ 0. Recall also that the nullspace oF matrix A is the set oF all vectors x s.t. Ax = 0. Now consider the reachability Gramian M R ( t ,t f ,A,B ) = i t f t Φ( t 1 ,τ ) B ( τ ) B T ( τ )Φ T ( t 1 ,τ ) dτ Show that nullspace( M R ( t ,t f ,A,B )) ⊂ nullspace( M R ( t 1 ,t f ,A,B )) For all t 1 ∈ ( t , t f ). Problem 7: Consider the continuous system: ˙ x ( t ) = p 1 0 2 3 P x ( t ) + p b 1 b 2 P u ( t ) Under what conditions on [ b 1 b 2 ] T is the system reachable? Problem 8: Consider a pair ( A,B ) where A ∈ R n × n and B ∈ R n × k , k < n . Show that iF A is diagnolalizable and has an eigenvalues oF multiplicity greater than k then the pair is not reachable....
View
Full
Document
This note was uploaded on 02/09/2010 for the course MAE 123 taught by Professor 123 during the Spring '10 term at École Normale Supérieure.
 Spring '10
 123

Click to edit the document details