Non-Lyapunov homogeneous SISO control design

Abstract

A simple method of single-input-single-output (SISO) homogeneous control design is proposed which does not employ Lyapunov technique and allows immediate easy construction of infinitely many homogeneous control forms for all relative and homogeneity degrees (HDs). In accordance with the HD the controllers feature finite-time or asymptotic stability, and fixed-time convergence to any vicinity of zero for positive HDs. Many known homogeneous sliding-mode controllers and finite-time stabilizers are obtained as particular cases. Computer simulation illustrates the theoretical results.