DelayTools.Duality

Based on the Paper:

SOS Methods for Multi-Delay Systems: A Dual Form of Lyapunov-Krasovskii Functional

Submitted to IEEE Transactions on Automatic Control.

[arXiv] [.pdf] [.ps]Introduction: A highly-optimized Matlab toolbox for enforcing positivity of Lyapunov functions for infinite-dimensional systems. Also contains fixes to Multipoly and SOSTOOLS.

This toolbox:

1. Requires Matlab 2011a or later.

2. Requires that a working version of SeDuMi be installed.

3. Requires the entire folder be placed in the path along with sub-folders.

4. Replaces any existing version of SOSTOOLS. No previous version should appear in the path.

5. Replaces any existing version of MULTIPOLY. No previous version should appear in the path.

[DelayTools_Duality_v1.zip]- DelayTools Package for Dual Stability Analysis

DelayTools.v06 (updated 10/09/2013)

Based on the Paper:

LMI Parameterization of Lyapunov Functions for Infinite-Dimensional Systems: A Toolbox

American Control Conference, 2014Introduction: A highly-optimized Matlab toolbox for enforcing positivity of Lyapunov functions for infinite-dimensional systems. Also contains fixes to Multipoly and SOSTOOLS.

This toolbox:

1. Requires Matlab 2011a or later.

2. Requires that a working version of SeDuMi be installed.

3. Requires the entire folder be placed in the path along with sub-folders.

4. Replaces any existing version of SOSTOOLS. No previous version should appear in the path.

5. Replaces any existing version of MULTIPOLY. No previous version should appear in the path.

[delaytools_10_09_2013.zip]- DelayTools Package

DelayTools.Linear.v04

Based on the Papers:

Positive Forms and Stability of Linear Time-Delay Systems

SIAM Journal on Control and Optimization

Stability Analysis of Linear Systems with Time-Varying Delays: Delay Uncertainty and Quenching

CDC 2007

Introduction: A matlab toolbox implementation of the algorithms described in the journal paper "Stability analysis for linear time-delay systems using semidefinite Programming" as submitted to SICON and also "Positive Quadratic Forms and the Stability of Linear Time-Delay Systems " as appears in CDC 2006. The zip file contains the main scripts linear_nd_ndelay.m and linear_nd_ndelay_uncertain for the fixed and uncertain cases as well as some supporting Matlab functions. Some Instructions for use are contained in the script headings. Full documentation is not yet available.

This toolbox requires a working version of the SOSTOOLS toolbox for matlab which can usually be found at http://www.cds.caltech.edu/sostools/. We also require you to fix a serious BUG in SOSTOOLS by replacing the file subs.m in sostools/multipoly/@polynomial with the attached file subs.m.

As part of the PVAR package, we have also developed a function for integration of PVAR symbolic variables: int_p.m. This function was left out of the SOSTOOLS PVAR toolbox.

The original version of this script requires a version of Matlab with Maple, i.e. ver 2007a or earlier. It WILL NOT WORK with 2007b+. We have now updated the software to work with Matlab 2007b and later.

[DelayTools.Linear.zip] - DelayTools Package

[DelayTools.Linear_pvar.zip]- DelayTools Package compatible with Matlab 2007b+. Note that you must patch SOSTOOLS as indicated above for this program to work.

[solver_1or2delay_tv_beta.m] - (Beta version) Add-on for systems with time-varying delay

DelayTools.Nonlinear.v00

Based on Chapter 8 of my thesis:

Stability and Control of Functional Differential Equations

Defended March 15, 2006

Introduction: A matlab toolbox implementation of the algorithms described in Chapter 8 of my thesis on delay-dependent stability analysis of nonlinear delay-differential equaitons. The zip file contains the main scripts nonlinear_nd_ndelay.m and nonlinear_nd_ndelay_uncertain for the fixed and uncertain cases respectively as well as some supporting Matlab functions. Instructions for use are contained in the script headings. This toolbox requires a working version of the SOSTOOLS toolbox for matlab which can usually be found at http://www.cds.caltech.edu/sostools/. Note: A general implementation of this script is still in development. Contact matthew.peet@inria.fr if interested for several examples.

[DelayTools.Nonlinear.zip]

DelayTools.Complex.v01

Based on the paper:

Using the Positivstellensatz for Stability Analysis of Neutral Delay Systems in the Frequency Domain

Published in the proceeding of the 7th IFAC workshop on time-delay systems

Introduction: A number of matlab toolbox functions for analysis of transfer functions in the frequency domain using SOS and positivstellensatz techniques. Scripts test quasiploynomial transfer functions for both delay-independant and delay-dependant H_infty stabiltiy and delay-independent exponential stability. The delay-dependent test is based on the paper by Zhang et al. This toolbox requires a working version of the SOSTOOLS toolbox for matlab which can usually be found at http://www.cds.caltech.edu/sostools/.

DelayTools.Synthesis

Based on the paper:

Full-State Feedback of Delayed Systems using SOS: A New Theory of Duality

Published in the proceeding of the 11th IFAC workshop on time-delay systems

Introduction: Matlab code for constructing a stabilizing full-state feedback controller for a time-delay system. Includes solver_dualstabilitytest.m - which tests stability using a dual criterion; solver_synthesistest.m - which solves the operator inequality; inverting_operators_scalar.m - which uses the output of the operator inequality to find the feedback gains. Note that inverting_operators_scalar.m requires the user to execute a mupad script manually, so please read the comments in this file carefully. Finally, a simulation code is included. Several other supporting files are included. Note this toolbox requires a working version of the SOSTOOLS toolbox for matlab which can usually be found at http://www.cds.caltech.edu/sostools/.