Prescribed-time practical stabilization via majorant systems

Abstract

This paper provides a design methodology of simple control laws to solve the prescribed-time practical stabilization problem for a class of pseudo-linear systems with a single input, also unstable, subject to perturbations, nonlinear and discontinuous, but bounded. The perturbations on the dynamic matrix, such as a ratio of multi-affine polynomials of nonlinear functions or parameters, are not triangular, and a perturbation on the input of multiplicative type is also considered. The stated methodology is based on the majorant systems approach with optimized quadratic Lyapunov functions. The main advantages of the proposed control laws consist in the simplicity of their design and implementation and the reliable performance. Indeed, these control laws depend on a single design parameter, have constant gains, and guarantee the practical convergence with a prescribed relative error, also after a prescribed time. Some examples, also an engineering one, are provided to validate the obtained theoretical results and show the effectiveness and efficiency of the proposed control laws.