Delay difference inclusions (DDIs) have received an increasing attention recently, mostly due to their ability to model a wide variety of relevant processes, including networked control systems. Therefore, in this presentation, the Lyapunov framework is used to discuss the concepts of stability and invariance for such systems. It is shown that stability can be investigated in a non-conservative manner based on the Krasovskii approach. However, when computational simplicity is preferred over conceptual generality, an attractive alternative for stability analysis is shown to be provided by the Razumikhin approach. The understanding that the Razumikhin approach is based on small-gain arguments allows us to uncover a relation to the Krasovskii approach. Similarly as for stability analysis, methods that favor either conceptual generality or computational simplicity also exist for set invariance methods. Some recently developed results yield a technique that provides a trade-off between the two aforementioned properties. Then, the above insights are applied to the stability analysis for large-scale interconnected systems. A tractable stability analysis method is obtained using a small-gain condition and either the Krasovskii or the Razumikhin approach. The application of these theorems to large-scale power systems with delays shows the practical applicability of the developed results.
Rob H. Gielen (born in Nijmegen, the Netherlands, 1984) received his M.Sc. degree (cum laude) in Control Engineering from the Eindhoven University of Technology, Eindhoven, The Netherlands in 2009. Currently, he is working towards the degree of Ph.D. in the Control Systems group of the Electrical Engineering Faculty at the same institution. His research interests include stability analysis and stabilizing controller synthesis for general delay discrete-time systems with applications to networked control systems, automotive systems and large-scale power systems. Recently, he was awarded a Fulbright fellowship to perform part of his research for the degree of Ph.D. at the University of California at Santa Barbara.