Chair HS


Systems, signals and control theory is an area of research that has roots in electrical engineering, mechanical engineering and mathematics, and also has applications in, for example, econometrics, process technology and informatics. An essential part of this area forms the study of coupled processes -- the dynamical behavior of the components and their interaction with each other and their environment. Besides the analysis of such systems, the problem often concerns the design of components in such a way that the interconnected system has certain desired properties. Problems of this type occur for example when we need to control the position of satellites or want to filter relevant information about the structure of earth layers from a seismic signal.

Control problems have been around for a long time. With the rise of automated manufacturing in the nineteenth century, control mechanisms gained in importance. Watt's fly-ball governor, a device that controls the steam pressure, meant a breakthrough and directly contributed to the industrial revolution. Up to this day the manufacturing of servo mechanisms plays an important part in mechanical engineering (e.g. in robot technology.) Within the electrical engineering community the need for a theoretical underpinning of the behavior of interconnected components arose through questions like: how may we mathematically model a (complicated) electrical circuit, and conversely, given a mathematical model, how may we implement it as an electrical device. Once mathematically formulated, it was found that the above problems of mechanical en electrical engineering had much in common and that in fact they belong to a single area, an area that nowadays is called systems and control. The mathematics of systems and control involve analytical as well as algebraic notions, possibly because "change over time" and "relation between quantities" both are central in systems and control problems.

In the past twenty five years systems and control has experienced a strong development. Applications no longer are restricted to electrical, mechanical and chemical engineering. In econometrics and time series analysis methods of system theory are used, controllers are designed to influence fermentation processes, and filters to estimate car densities on high ways are being developed. Furthermore, due to the impact of computer science, new control problems have emerged on the interface between control and informatics. The mathematical disciplines explored by system theoreticians have diversified. They range from Hilbert spaces to Bezout domains, from analytical functions to probability measures and from Lie groups to Petri nets.