Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

Abstract

The design of delay-dependent robust H∞ controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to H∞ performance analysis and robust H∞ controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.