This preview shows page 1. Sign up to view the full content.
Unformatted text preview: happen that there exists an input taking an initial state x into the origin in k time steps, but there does not exist one that does it in k1. (b) Derive conditions for discretetime controllability, modifying the definition accordingly so the transfer between states should be made in k n time steps. P6. Show that ( A, B ) is controllable if and only if W t is positive denite, i.e., W t &gt; 0, for all t &gt; 0. P7. Let A be stable. Show that ( A, B ) is controllable if and only if the solution P of the Lyapunov equation AP + P A * =BB * is positive denite. Show that the matrix P is equal to the limit of the gramian W c ( t 1 ), when t 1 ....
View
Full
Document
This note was uploaded on 01/04/2012 for the course CDS 212 taught by Professor Tarraf,d during the Fall '08 term at Caltech.
 Fall '08
 Tarraf,D

Click to edit the document details