{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw2 - J.M Gonalves c Winter 2004 CDS 213 Robust Control...

This preview shows pages 1–2. Sign up to view the full content.

J.M. Gon¸ calves Winter 2004 CDS 213 - Robust Control Homework # 2 Date Given: February 5th, 2004 Date Due: February 19th, 2004 P1. Prove corollary 6.6 in DP p. 204. Also, prove that H is in the domain of the Riccati operator if and only if ( A, B ) is stabilizable and ( C, A ) has no unobservable modes on the imaginary axis. Also prove that Ker( X ) = 0 if and only if ( C, A ) has no stable unobservable modes (if you get stuck, and only after thinking about it for some reasonable time, you are allowed to look into theorem 12.4 in Zhou). P2. Do question 6.7, DP, p. 214. P3. Let A R m × m , B R n × n and C R m × n be given and consider the Sylvester Equation AX + XB = C for an unknown matrix X R m × n . Let M = B 0 C - A , N = B 0 0 - A . 1. Let the columns of U V C ( n + m ) × n be the eigenvectors of M associated with the eigenvalues of B and suppose U is nonsingular. Show that X = V U - 1 solves the Sylvester Equation. Every solution of the Sylvester Equation can be written in the above form.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw2 - J.M Gonalves c Winter 2004 CDS 213 Robust Control...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online