User:Egm6321.f10.team4.Yoon/Mtg14

=EGM6321 - Principles of Engineering Analysis 1, Fall 2010=

SC-L1-ODE-VC and SC-L1-ODE-CC
 Mtg 14: Thu, 23 Sep 10

[[media: 2010_09_23_13_57_17.djvu | Page 14-1]]
Linear Time-Invariant system $$\displaystyle \equiv$$ SC-L1-ODE-CC Linear Time-Variant system $$\displaystyle \equiv$$ SC-L1-ODE-VC

Particular case: When n=1 (L1-ODE-VC)

Open loop: u(t) is prescribed.

L1-ODE-VC: Varying coefficients

SC-L1-ODE-CC: Constant coefficients

[[media: 2010_09_23_13_57_17.djvu | Page 14-2]]
Recall: 

Bryson&Ho 1975 p.450

Compare [[media: 2010_09_23_13_57_17.djvu | Eqn.(3) to Eqn.(4) p.14-1]] (Constant Coefficients)

[[media: 2010_09_23_13_57_17.djvu | Page 14-3]]
$$\displaystyle \mathbf{\Phi} $$ is related to Integrating Factor

Prop. of $$\displaystyle \color{blue}{\mathbf{\Phi}(t, t_0)}$$: (State transition matrix)

Recall SC-L1-ODE-CC