Week 03
State Transition and Response
I use the saved simulation video as a starting point to revisit state-space control, observers, and digital control.
What I connect in this unit
The state-transition matrix propagates the initial state, while the input convolution contributes the zero-state response. Eigenvalues of A define the modes inside e^(At), linking state motion to growth, decay, and oscillation.
Concept map
- Matrix exponential
- Zero-input response
- Zero-state response
- Eigenvalues
Technical anchor
The solution is x(t)=e^(At)x(0)+∫[0,t]e^(A(t-τ))Bu(τ)dτ. Separate the two terms and identify how each eigenvector direction carries an e^(λt) mode.
How I review it
Begin with a diagonal A, verify that the transition matrix equals I at t=0, and substitute the resulting x(t) back into the state equation.
Connection to the full course
Unit 3 of 12. This study sequence connects the system flow visible in the video with standard control topics; it is not a claim about lecture weeks.