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: Show that the origin of (1) is asymptotically stable if in a neighborhood of the origin, there is a continuous positive denite function V ( x ) so that V ( x ) is negative denite. Consider the linear discretetime system: x k +1 = Ax k . Show that the following statements are equivalent: * x = 0 is asymptotically stable. *  i  &lt; 1 for all eigenvalues of A . * Given any Q = Q T &gt; 0, there exists P = P T &gt; 0, which is a unique solution to the linear equation A T PAP =Q ....
View
Full
Document
This note was uploaded on 01/04/2012 for the course CDS 140A taught by Professor Marsden during the Fall '09 term at Caltech.
 Fall '09
 Marsden

Click to edit the document details