Output feedback synthesis for sampled-data system with input saturation

In this paper we address the sampled-data regional and global H∞ synthesis problem for a class of linear plants subject to input saturation, where the sampling and hold rates are synchronous. Such a sampled-data system is expressed as a jump system, which is further described as a class of hybrid systems. Based on Lyapunov theorems for hybrid systems, a Lyapunov function is constructed and it is proved that the H∞ problem is equivalent to a purely discrete-time synthesis problem. The proposed synthesis approach is cast as a convex optimization over Linear Matrix Inequalities (LMIs), which leads to an output feedback controller with an internal deadzone loop, achieving stability and desired performance. The effectiveness of the proposed techniques is illustrated by one example consisting in a mechanical system with different sample-and-hold rates.