Attraction domain estimation of linear controllers for the attitude control of VTOL vehicles: P/PI control of a quadrotor

Abstract

In this paper, we present a numerical method based the Lyapunov theory to estimate the attraction domain of a class of nonlinear systems. This problem is motivated by the analysis of linear attitude controllers for the control of Vertical Take-Off and Landing (VTOL) vehicles such as quadrotors. These linear controllers are typically designed in order to ensure local stability around the hover point. The purpose of this work is to estimate their attraction domain around this point. The proposed attraction domain estimation method requires to solve a convex optimization problem involving parameter-dependent Linear Matrix Inequalities (LMI). This problem is generally difficult to solve as it is an infinite dimensional optimization problem. However, we reveal that the specific structure of the VTOL vehicles attitude model can be exploited to make this LMI problem finite dimensional and thus numerically solvable.