Software for analysis and control of time-delay systems

Software package TDS-CONTROL


TDS-CONTROL is an integrated Matlab package for the analysis and controller-design of linear time-invariant (LTI) dynamical systems with discrete delays. The presented toolbox can deal with a broad class of time-delay systems, including both systems of retarded and neutral type. These systems are assumed to be given in state-space form, although functionality is provided to obtain such a representation from a frequency-domain description of the system. Firstly, the package offers various methods to analyze LTI time-delay systems. More specifically, it contains methods for computing the spectral abscissa, the H-infinity norm, the pseudospectral abscissa, and the distance to instability. As TDS-CONTROL is designed with neutral delay differential equations in mind, it has the appealing feature that the sensitivity of certain quantities (such as the spectral abscissa) with respect to infinitesimal delay perturbations can explicitly be taken into account. Secondly, besides the analysis tools mentioned above, TDS-CONTROL also contains functionality to design fixed-order dynamic output feedback controllers for which the order of the controller may be smaller than that of the plant. As a consequence, also static output feedback controllers (which have order zero) can be considered. These controller-design algorithms are based on optimizing the spectral abscissa, the H-infinity norm or a combination of both with respect to the free controller parameters. For example, to design a (strongly) stabilizing controller the (strong) spectral abscissa is minimized. Furthermore, this optimization-based approach allows to easily impose structure on the controller, which enables the design of decentralized and proportional-integral-derivative (PID) controllers. Finally, by allowing the plant to be described in delay descriptor form (i.e., time-delay systems for which the evolution of the state variable is described by described by delay differential-algebraic equations), Pyragas-type, acceleration and delay-based feedback controllers can be considered.


TDS-CONTROL is rooted in the Laplace-domain framework for the analysis and controller-design of LTI time-delay systems presented. More specifically, TDS-CONTROL considers MIMO time-delay systems given in state-space representation that may have multiple delays in the state, input, and output terms. It can deal with both retarded and neutral time-delay systems, and even with (certain) systems in delay descriptor form (i.e., described by delay-differential algebraic equations). It can also automatically convert a SISO transfer function (ratio of quasi-polynomials) representation to a state-space representation. For these systems, TDS-CONTROL provides the following functionality:

To this end TDS-CONTROL provides the following functions:


TDS-CONTROL was written by Pieter Appeltans, under the supervision of Haik Silm and Wim Michiels. It integrates several methods and algorithms that have been developed in the research group of W. Michiels (NUMA - Numerical Analysis and Applied Mathematics Section, KU Leuven) since 2008.


The software package, installation instructions and documentation are available from this page.

For a direct link to the manual, with a tutorial flavor on spectral properties and control of time-delay systems, click here.

Usage and citation

In published work relying on the use of TDS-CONTROL, the authors must refer to the following two articles.
  1. P. Appeltans, H. Silm and Wim Michiels. TDS-CONTROL: a MATLAB package for the analysis and controller-design of time-delay systems, IFAC-PapersOnLine, 55(16), 272-277, 2022.
  2. P. Appeltans and W. Michiels. Analysis and controller-design of time-delay systems using TDS-CONTROL. A tutorial and manual. e-Print arXiv:2305.00341, 2023.

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This page is maintained by Wim Michiels.
Last updated in May 2023.