Nonlinear output feedback control laws based on linear ones for improving ultimate bound.

In this paper, we design nonlinear output feedback control laws obtained from linear ones by using two types of replacements. These replacements use some kinds of odd nonlinear functions and do not change the tuning coefficients calculated in the linear control law. The first replacement consists of passing each component of the output vector through a nonlinear function, and the second replacement consists of passing each component of the linear control law through a nonlinear function. As a result, the proposed nonlinear control laws reduce the ultimate bound compared to the linear controller. A novel method is proposed to study such control schemes. This method consists in representing nonlinear functions as linear ones with nonlinear slopes, that allows the use of linear matrix inequality (LMI) approaches to study the stability of the closed-loop system. The stability and attraction domains are found by using a new multi-step procedure based on the verification of the LMI feasibility in subdomains, the union of which gives the searched domains. The simulations confirm the theoretical results and illustrate the efficiency of the proposed methods compared to some linear controllers. [ABSTRACT FROM AUTHOR]