Input-Output Stability Analysis of Networked Control Systems

The main focus of the thesis is to derive stability criteria for networked control system (NCS) models featuring imperfections such as time-varying and constant delays, quantization, packet dropouts, and non-uniform sampling intervals. The main method of proof is based on matrix algebra, as opposed to methods using Lyapunov functions or integral quadratic constraints (IQC). This work puts a particular focus on handling systems with a single integrator. This framework is elaborated in different specific directions as motivated by practical realizations of NCSs, as well as through numerical examples. A novel proof of the discrete time multivariate circle criterion and the Tsypkin criterion for systems including a single integrator is presented, as well as a stability criterion for linear systems with a single integrator subject to variable sampling periods and sector-bounded nonlinear feedback. Four stability criteria for different classes of systems subject to packet loss and time-varying delay are given. Stability criteria for a closed loop system switching between a set of linear time-invariant systems (LTIs) are proved. This result is applied to a single-link NCS with feedback subject to packet loss. Finally, necessary and sufficient conditions for delay-independent stability of an LTI system subject to nonlinear feedback are derived.