  The paper investigates nonlinear control laws obtained from linear one by two
types of substitutions using odd functions. The first substitution consists in
passing each component of the state vector through a nonlinear function, the
second substitution is in passing the entire linear control law through a
nonlinear function. To study such systems, it is proposed to represent
nonlinear functions as linear ones with a nonlinear slope. Such a
representation will make it possible to use the linear matrix inequalities
(LMIs) to study the stability of the closed-loop systems. The stability regions
and the regions for the initial conditions are found, which are obtained as a
result of a multistep procedure for finding solutions of LMIs. It is shown that
the use of the proposed nonlinear control laws makes it possible to reduce the
steady-state error in comparison with the linear ones.
