{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

problem6 - EE221A Linear System Theory Problem Set 6...

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

View Full Document Right Arrow Icon
EE221A Linear System Theory Problem Set 6 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2007 Issued 11/6; Due 11/15 Problem 1: Stiff Differential Equations. In the simulation of several engineering systems we encounter parasitic elements which result in the differential equation becoming “stiff”, for example, parasitic capacitances and inductances in electronic circuits. Consider the elementary circuit of Figure 1 with epsilon1 being a small parasitic capacitance. Write down the state equations for the circuit using x 1 and x 2 as state variables. Note that the A matrix depends on epsilon1 and that some of its elements blow up as epsilon1 0. Show that asymptotically one of the eigenvalues of A is of the order 1 /epsilon1 and the other is of order 1. Now generalize this example to the system ˙ x 1 = A 11 x 1 + A 12 x 2 epsilon1 ˙ x 2 = A 21 x 1 + A 22 x 2 with x 1 R n , x 2 R m , and A 22 nonsingular. Show that m eigenvalues go to as epsilon1
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern