1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find State Transition Matrix (time variant)

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data
    find the state transition matrix of a time varying system where:
    dX/dt = A*X

    with A = [-1 , exp(-t - (t^2)/2) ; ; 0 , t] (Matlab format - sorry but its easier)

    2. Relevant equations
    How to go about solving such problems in a systematic way???

    3. The attempt at a solution
    I've found eigen values of (-1) and (t), and associated eigen vectors of [1 ,0]T and [exp(-t - (t^2)/2) , (t+1)]T......which lead me to one solution vector of [exp(-x) , 0]T....and having trouble getting the other one. HOWEVER, i'm just "bushwhacking" here....I need some help in figuring out a systematic approach.

    Thanks!!
     
  2. jcsd
  3. Oct 6, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The two columns ##\vec{x}_1## and ##\vec{x}_2## of ##X## are solutions of
    [tex] \frac{d}{dt} \pmatrix{x\\y} = \pmatrix{-1 &\exp(-t - t^2/2)\\0 & t } \pmatrix{x\\y} [/tex]
    Expanding it out, the DE for ##y## is simple enough to solve; then substitute the solution ##y(t)## into the first equation and solve that.
     
    Last edited: Oct 6, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find State Transition Matrix (time variant)
Loading...