Design of nonlinear selectively invariant systems based on the controllable Jordan form

A method to design the nonlinear control systems that are selectively invariant to the unmeasurable bounded perturbations with a certain $K(p)$-image was proposed. The perturbations may be arbitrary, but their order should not exceed the value established at the design. The nonlinear control is generated relying on the state variables of the extended plant and the estimates of the state variables of a virtual system that is equivalent to the extended plant. A numerical example of design was presented.