A Further Result on Semi-global Stabilization of Minimum-Phase Input–Output Linearizable Nonlinear Systems by Linear Partial State Feedback

It has been established that a globally asymptotically stable nonlinear system cascaded by a controllable linear system through its output can be semi-globally asymptotically stabilized by linear feedback of the state of the linear subsystem as long as the linear system is right invertible and has all its invariant zeros located on the closed left-half plane. In particular, a globally asymptotically stable nonlinear system cascaded by a chain of integrator through the state of any one integrator or the control input is semi-globally asymptotically stabilizable by linear feedback of the states of the integrators. In this note, we show that the restriction on the interconnection between the linear and nonlinear subsystems can be further relaxed. For example, a globally asymptotically stable nonlinear system cascaded by a chain of integrator can still be semi-globally stabilized even when the cascade is through the states of two consecutive integrators, with the input regarded as an additional state following the last integrator.