Multiple?input multiple?output homogeneous integral control design using the implicit Lyapunov function approach

In this article, continuous and discontinuous integral controllers for multiple-input multiple-output (MIMO) systems are designed a large class of nonlinear systems, which (partially) feedback linearizable. These arbitrary positive or negative degree homogeneity derived by combining Lyapunov function obtained from the implicit (ILF) method with some extra explicit terms. Discontinuous able to stabilize an equilibrium track time-varying signal in finite time, while rejecting vanishing uncertainties nonvanishing Lipschitz matching perturbations. Continuous achieve asymptotic stabilization despite constant perturbations finite-time, exponentially nearly fixed-time negative, zero, degree, respectively. The design properties different classes illustrated means simulation example.