TDS-CONTROL: a MATLAB package for the analysis and controller-design of time-delay systems*

This paper presents TDS-CONTROL, a MATLAB package for the analysis and design of controllers for linear time-invariant systems with discrete delays. The code is based on a state-space representation of such systems in terms of delay-differential algebraic equations with input, output, and state delays. As such, a broad class of (interconnected) systems can be considered, including neutral systems. The controller design algorithms are based on optimizing a certain objective function, such as the spectral abscissa, the H-infinity norm, or the pseudo-spectral abscissa, with respect to the controller parameters. For example, to design a stabilizing controller the spectral abscissa, i.e., the real part of the right-most characteristic root, is minimized. As a strictly negative spectral abscissa is a necessary and sufficient condition for stability, the presented design method is not conservative and a stabilizing controller can be computed whenever it exits. This comes however at the cost of having to solve a non-smooth, non-convex optimization problem. The class of considered controllers consists of static and dynamic output-feedback controllers. By allowing to fix certain entries in the controller matrices, it is also possible to design structured controllers such as decentralized, overlapping and PID controllers. Finally, as a wide-range of delay systems can be considered, the software package takes the sensitivity of certain quantities, such as the spectral abscissa and the H-infinity norm, with respect to infinitesimal delay perturbations explicitly into account.