Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems
using Sum-of-Squares Optimization

by Zachary Jarvis-Wloszek

Download the thesis: zwjthesis.pdf
Download the talk: zwjtalk.pdf

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The code for all the examples in the thesis is provided below. A variety of matlab packages are needed to run the code. We avoid using matlab's symbolic library by using the polynomial class written by Pete Seiler, and the particular version we use is here. The polynomial class interfaces with SOSTOOLS to set up Sum-of-Squares (SOS) optimization problems as Semi-Definite Programs (SDPs) which are solved by SeDuMi . Some versions of SOSTOOLS have iffy support for the polynomial class, so the version we use is here.


To run the examples below:
1) Download and install SeDuMi. Adjust your path to include its functions
2) Download and install SOSTOOLS. Adjust your path to include its functions
3) Download the polynomial class and make sure it is in your path
4) Download and expand the directory of m functions: fns.tar. Adjust your path to include it.


Stability Analysis
Semi-Global Exponential Stability from 3.2.1 (sgestab.m)
Local Asymptotic Stability from 4.2.3 (asstabD.m, asstabI.m)
Discrete Time Set Invariance from 5.1.1 (setinvar.m)
Discrete Time Local Asymptotic Stability from 5.3.3 (dtstabD.m, dtstabI.m)

Disturbance Analysis
Global Induced L2->L2 Gain Bound from 3.4.3 (sfL2bound.m) and 3.5.2 (ofL2boundV.m, ofL2boundK.m)
Bounding Maximum Disturbance Peak for Set Invariance from 4.4. (localpeak.m, localpeak-results.mat)
Local Induced L2->L2 Gain Bound from 4.4.3 (localL2bound.m)
Discrete Time Set Invariance under Disturbances from 5.1.3 (setinvarw.m)

State Feedback Controller Design
Semi-Global Exponential Stabilization from 3.4.2 (bilinex.m) and 3.4.3 (sgesfV.m, sgesfV-results.mat, sgesfK.m, sgesfK-results.mat)
Local Asymptotic Stabilization from 4.4.3 (assfD.m, assfD-results.mat, assfI.m, assfI-results.mat))

Output Feedback Controller Design
Semi-Global Exponential Stabilization from 3.5.2 (sgeofV.m, sgeofV.mat, sgeofK.m, sgeofK.mat, sgeofKlow.m, sgeofKlow.mat)
Local Asymptotic Stabilization from 4.5.3 (asofD.m, asofD-h1-results.mat, asofD-h2-results.mat, asofI.m, asofI-h1-results.mat, asofI-h2-results.mat)