A [K, KL] sector based control design for nonlinear system. (June 2019) - Sachan, Ankit; Kamal, Shyam; Singh, Devender; Xiong, Xiaogang
Abstract: A new approach for asymptotic stabilization of a general input-affine nonlinear system is presented. This relies upon the results of Matrosov's theorem to decompose the n th dimensional space. The construction of the [K, KL] sector for a nonlinear system is done with the suitable choice of control-Lyapunov function. The study of a nonlinear system is viewed from the perspective of comparison function for uniformity in solution. By means of designed sector, we design a switching controller which is well suited in the condition that shows its presence only outside of [K, KL] sector. Thus, it yields a stabilization scheme which saves the superfluous control termed as Lazy or Hands-Off control. Finally, we demonstrate the proposed approach which yields an asymptotically stable results for the simulation of an illustrative example. Highlights: The definition of [K, KL] sector with a K ∞ class function. The equivalence definition of [K, KL] sector with the comparison of two K ∞ class functions. The elementary [K, KL] sector based on the above equivalence definition. The design specification of elementary [K, KL] sector. A new approach to design [K, KL] sector.