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.
- Lecture handout
- MATLAB code: phaseplot.m, boxgrid.m, L3_1_stability.m, oscillator.m, invpend.m, predprey.m
Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.
- K. J. Åström and R. M. Murray,, Preprint, 2007..
- Homework #3
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.