A [K,KL] sector based control design for nonlinear system

Ankit Sachan; Shyam Kamal; Devender Singh; Xiaogang Xiong

doi:10.1016/j.isatra.2018.12.017

A [K,KL] sector based control design for nonlinear system

ISA Trans. 2019 Jun:89:77-83. doi: 10.1016/j.isatra.2018.12.017. Epub 2018 Dec 14.

Authors

Ankit Sachan¹, Shyam Kamal¹, Devender Singh¹, Xiaogang Xiong²

Affiliations

¹ Department of Electrical Engineering, Indian Institute of Technology (BHU), Varanasi, U.P., India.
² Department of Mechanical and Automation, Harbin Institute of Technology, Shenzhen, PR China. Electronic address: xiongxg@hit.edu.cn.

PMID: 30598322
DOI: 10.1016/j.isatra.2018.12.017

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 nth 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.

Keywords: sector; Asymptotic stability; Control-Lyapunov function; Lazy or Hands-Off control.