Robustness of Nonlinear Control Systems to Network-Induced Imperfections

Nowadays control systems are increasingly implemented over shared resource-constrained communication networks. Namely, sensors, controllers and actuators no longer exchange information through dedicated point-to-point connections but compete for network access, which gives rise to network-induced imperfections that adversely affect control performance. Prevalent network phenomena are scheduling protocols, nonuniform variable delays, quantization, packet dropouts, sampled and distorted data. Besides possessing usual robustness requirements (e.g., to modeling uncertainties or external disturbances), such control systems ought to be robust against the aforementioned network phenomena as well. This article brings a methodology to quantify control system robustness via Lp-gains as the control laws, communication delays, sampling intervals, noise levels or scheduling protocols change. Building upon impulsive delayed system modeling, Lyapunov stability and the small-gain theorem, the proposed methodology takes into account nonlinear time-varying dynamic controllers and plants as well as model-based estimation, output feedback and large delays. The inverted pendulum example is provided.