Stability of interconnected time-varying systems

• Applicant: Professor Dr. Sergey Dashkovskiy
• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 581983951

This project is devoted to stability investigations of coupled non-autonomous infinite dimensional systems. There are only few results in the literature in this field, providing sufficient stability conditions of the small-gain type. However these results do not pay particular attention to such situations, when the coupling between subsystems can be switched on / off periodically or is of oscillating nature, which is very relevant for practical applications. Also in practice it may happen that subsystems appear and disappear from a net- worked. In such situations the existing stability results are either too conservative or even not applicable at all in order to conclude about stability properties of the network. In our research we will develop a new concept, which we call integral gain, with quantifies interactions between subsystems in a more flexible way than the in existing works. Moreover, the stability conditions to be developed in this project are based on essentially new type of construction of Lyapunov function for the interconnection. To cope with systems governed by unbounded operators we will need to deal with non-coercive Lyapunov functions. We expect to obtain stability results for wide classes of linear and non-linear time varying infinite dimensional systems including interconnections of PDEs, ODEs and integro-differential equations.

• DFG Programme: Research Grants