Nonlinear Stabilization: Control Contraction Metric Approach via Sum of Square Programming Technique

The study in this article focuses on the stability and performance of nonlinear uncertain system. Control contraction metric (CCM)approach is the latest ongoing trend in the field of design and stability of nonlinear systems. Unlike other nonlinear stability and design approach, contraction analysis deals with stability that is defined incrementally between two arbitrary independent trajectories. In this approach, CCM is found via sum of square (SOS)programming using SOSTOOLS and semi definite programming solver SeDuMi. The said design is validated on the nonlinear model of Moore-Greitzer jet engine. The said approach ensures better overall transient performance compared to that of linear quadratic regulator (LQR)controller independent of initial conditions confirming universal stability of CCM. Also, with the increase in the degree of polynomial of contraction metric, system performance is found to be better compared to that of lower degree polynomial.