A polynomial approach for analysis and optimal control of switched nonlinear systems (2009)
"In this dissertation, we investigate how convex semialgebraic geometry and global polynomial optimization can be used to analyze and to design switched nonlinear systems. To deal with stability analysis of switched nonlinear systems it is shown that the representation of the original switched problem into a continous polynomial system allows us to use the dissipation inequality for polynomial systems. With this method and from a theoretical point of view, we provide an alternative way to search for a common Lyapunov function for switched nonlinear systems. The main idea behind the proposed approach is to include in the system analysis the hidden constraints... "