Local performance analysis of uncertain polynomial systems with applications to actuator saturation

This paper considers the local performance analysis of uncertain polynomial systems. A method for estimating an upper bound of the local L₂ → L₂ gain is presented. The gain upper bound condition is formulated in terms of a dissipation inequality that incorporates an integral quadratic constraint to model the uncertainty. For polynomial systems, the dissipation inequality can be verified using sum-of-squares optimizations. This approach is applied to systems with actuator position and rate limits. The effectiveness of the proposed method is demonstrated on two numerical examples.