  This paper presents the design of an extremum seeking controller based on
sliding modes and cyclic search for real-time optimization of non-linear
multivariable dynamic systems. These systems have arbitrary relative degree,
compensated by the technique of time-scaling. The resulting approach guarantees
global convergence of the system output to a small neighborhood of the optimum
point. To corroborate with the theoretical results, numerical simulations are
presented considering a system with two inputs and one output, which rapidly
converges to the optimal parameters of the objective function.
