Plant-Order Saturated Output-Feedback Regional Controller Synthesis With Sign-Indefinite Quadratic Forms

This note provides tools to design a dynamic plant-order output-feedback controller for linear plants subject to saturating input with measurable output. Based on Linear Matrix Inequalities (LMIs), together with appropriate transformations and sector conditions, the proposed solution exploits sign-indefinite quadratic forms to define a locally positive definite piece-wise Lyapunov function providing non-ellipsoidal estimates of the closed-loop basin of attraction. With guaranteed local exponential stability, methods to ensure a prescribed local exponential convergence rate and to maximize the estimates of the region of attraction are also given.