Control for partial state constraining of nonlinear systems in regular form

A method for enforcing non-symmetrical constraints on the first block of the state of a nonlinear system in regular form is presented. Two cases are considered: the first block of the system stays within some arbitrarily selected limits, a) displaying a conservative behavior, shown as limit-cycle plots, and b) some sort of damping is introduced, forcing the second block of the state to tend to zero as time increases. Both cases emerged from a convenient selection of the stabilizing function in the control law. Simulation results present the closed-loop behavior of an open-loop unstable MIMO system, showing the effectiveness of the approach.