Control synthesis for non-polynomial systems: A domain of attraction perspective

This paper studies a control synthesis problem to enlarge the domain of attraction (DA) for non-polynomial systems by using polynomial Lyapunov functions. The basic idea is to formulate an uncertain polynomial system with parameter ranges obtained form the truncated Taylor expansion and the parameterizable remainder of the non-polynomial system. A strategy for searching a polynomial output feedback controller and estimating the lower bound of the largest DA is proposed via an optimization of linear matrix inequalities (LMIs). Furthermore, in order to check the tightness of the lower bound of the largest estimated DA, a necessary and sufficient condition is given for the proposed controller. Lastly, several methods are provided to show how the proposed strategy can be extended to the case of variable Lyapunov functions. The effectiveness of this approach is demonstrated by numerical examples.