State-transition matrix: Difference between revisions

Revision as of 04:28, 23 February 2013

Revision as of 05:30, 23 February 2013

Line 14:

:<math>\mathbf{x}(t)=\mathbf{\Phi}(t, \tau)\mathbf{x}(\tau)</math>

While the state transition matrix \&phi; is not completely unknown, it must always satisfy the following relationships:

:<math>\frac{\partial \phi(t, t_0)}{\partial t} = A(t)\phi(t, t_0)</math> and

Line 20:

:<math>\phi(\tau, \tau) = I</math> for all <math>\tau</math> and where <math>I</math> is the [[identity matrix]].<ref>{{cite book|first=Roger W.|last=Brockett|title=Finite Dimensional Linear Systems|publisher=John Wiley & Sons|year=1970|isbn=978-0-471-10585-5}}</ref>

And &phi; also must have the following properties:

:{| class="wikitable"