Homogeneous feedback design of differential inclusions based on control Lyapunov functions

• An improved formula of controllers based on control Lyapunov functions is presented.
• A homogeneous controller of homogeneous differential inclusions is designed.
• A homogeneous controller of differential inclusions with uncertainties is constructed.

This paper is concerned with the stabilization of differential inclusions. By using control Lyapunov functions, a design method of homogeneous controllers for differential equation systems is first addressed. Then, the design method is developed to two classes of differential inclusions without uncertainties: homogeneous differential inclusions and nonhomogeneous ones. By means of homogeneous domination theory, a homogeneous controller for differential inclusions with uncertainties is constructed. Comparing to the existing results in the literature, an improved formula of homogeneous controllers is proposed, and the difficulty of the controller design for uncertain differential inclusions is reduced. Finally, two simulation examples are given to verify the preset design.