Robustness-verification in networked control systems via sum-of-square approach

This paper discusses an approach for closed loop robustness evaluation of nonlinear networked control systems (NCSs). The continuous-time nonlinear multi-input plant is controlled via several predesigned nonlinear discrete-time controllers which are connected to the plant through a time-triggered communication network. In particular, the communication scheduling for the actuator signals are considered. Input-multiplicative uncertainty is investigated using an l₂-gain approach. For this, an overall model of the closed-loop system is derived. The plant is discretized using a Lie-algebraic approach, while a model of the communication network and the actuator uncertainty is augmented to the discrete plant. A lifting approach allows for nonlinear Lyapunov based l₂-gain computation using a Sum-of-Square (SOS) optimization. A numerical example shows the effectiveness of the approach.