CDS 101/110 - Dynamic Behavior
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This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.
Wednesday: Stability Analysis (Slides, MP3)
Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts; domain specific examples will be presented in individual recitation sections.
Friday: Lyapunov Stability (Slides, MP3)
|Monday|| Wednesday (CDS 110)
- K. J. Åström and R. M. Murray,, Preprint, 2006..
This homework set covers stability and performance through a series of application examples. The first problem provides a set of three real-world models in which the student must identify the equilibrium points and determine stability of the equilibrium points (through simulation). The second problem explores performance specification in the conext of the cruise control example, including step response and frequency response.
- Are the dynamics on slide 10 correct?
- Has a stable system a stable eq. point? a limit cycle?
- How are the z variables defined on slide 10, Lecture 3-1?
- How do equations given for dynamics on slide 10 relate to the state-space setup we used before?
- How do we choose epsilon in the definition of stability?
- How was V(x) derived on slide 13 of Lecture 3-1?
- Is the overshoot definition on slide 12 correct?
- Is the system on slide 5 stable?
- What is "closed form"?
- What is a plant in the context of this class?
- What is a stable system?
- Who/What is Lyapunov?
- Could you please make it clear what is an 'A' and what is a 'Lambda' (matrix)?
- Do complex matrices also have a Jordan canonical form?
- How do you actually find the Jordan canonical form of a matrix?
- I keep getting mixed up on whether the diagonalized form of A is T^(-1)AT or TAT^(-1). Is there an easy way to remember the correct form?
- Was the equation for V(q) for the spring mass example missing a transpose?
- What does "up to permutations" mean?
- Where can I find the proof to the Lyapunov Theorem?