An algorithmic approach for lessening conservativeness of criteria determining absolute stability

Lur´e systems are the feedback interconnection of a linear time-invariant system with a memoryless static operator. In this paper, we derive an algorithmic method to incorporate the information given by additional Lyapunov functions in order to enlarge the estimate of the domain of attraction of a Lur´e system. The methodology, limited for simplicity to quadratic Lyapunov functions, relies on the solution of a sequence of convex optimization programs. The ideas formulated in this article have general validity and can be extended to other scenarios (for example considering Lyapunov functions in the form of sum of squares.