Robust PI design for chaos control using sum of squares approach

This paper deals with the problem of designing a robust proportional-integral controller for a Lorenz chaotic system. The design methodology is based on a so called density function and formulated as a convex optimization program and solved by using sum of squares techniques. The robustness is guaranteed by exploiting parametric uncertainty bounds in design formulations in a manner similar to S-Procedure. The performance of the system is then examined using numerical examples. The innovation in this paper is the PI structure of the controller, which is simple and highly popular in engineering practices, and the use of nonlinear formulations, which makes the design non-conservative.