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:

- Non-conservative assessment of stability by means of the characteristic roots and the spectral abscissa.
- Computation of zeros.
- Strong stability analysis of neutral delay differential equations, i.e., the effect of (sufficiently) small delay pertubations can explicitly be taken into account.
- Stabilization by means of fixed-order dynamic output feedback controllers.
- Design of structured controllers like delay-based, acceleration and PID controllers.
- Performance and robust stability analysis by means of the H-infinity norm, the pseudospectral abscissa, and the distance to instability.
- Robust controller design through H-infinity norm optimization.
- Model order reduction and approximation.

- tds_create, tds_create_neutral, and tds_create_ddae: create a representation for retarded, neutral, and delay descriptor systems
- tds_roots: computes the characteristic roots in a given right half-plane or rectangular region
- tds_sa and tds_strong_sa: compute the (strong) spectral abscissa
- tds_tzeros: computes the transmission zeros of a SISO time-delay system
- tds_stabopt_static and tds_stabopt_dynamic: synthesize stabilizing static and dynamic output feedback controllers
- tds_hinfnorm: computes the (strong) H-infinity norm
- tds_hiopt_static and tds_hiopt_dynamic: synthesize static and dynamic output feedback controllers that minimize the closed-loop H-infinity norm
- tds_psa computes the pseudospectral abscissa of uncertain retarded time-delay systems with real-valued and and structured uncertainties on both the system matrices and the delays
- tds_dist_ins computes the distance to instability of uncertain retarded time-delay systems with real-valued and and structured uncertainties on both the system matrices and the delays

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

- 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. - 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.

- Evaluating and approximating FIR filters
- Design of input shapers with distributed delays
- Stability optimization of uncertain delay equations (probabilistic setting)
- Computing the robust H-infinity norm
- Computing the Floquet pseudospectral radius for periodic time-delay systems
- Design of strongly stable PID controllers
- Solving multi-parameter eigenvalue problems
- Calculating the minimal/maximal eigenvalue of symmetric parametrized matrices using projection
- Structure preserving shift-invert infinite Arnoldi method for delay eigenvalue problems with Hamiltonian symmetry

This page is maintained by Wim Michiels.

Last updated in May 2023.