Global Stabilization of Nonlinear Systems with Byrnes—Isidori Normal Form

1　IntroductionThe problem of the asymptotic stabilization of minimum phase nonlinear systems viasmooth state feedback has been well studied in1— 6 ].One major methodology is by useof the nonlinear analog of the nonlinear zero dynamics notion so that,un…

Global Stabilization of Nonlinear Systems with Byrnes-Isidori Normal Form

The global stabilization of nonlinear cascade systems with partially linear composite dynamics is discussed in this paper using continuous terminal sliding modes (TSM). A two phase control strategy is proposed. The first phase is to use a linear control, called pre-TSM control, to bring the system state into a region where the TSM control is not singular. The second phase is to employ the TSM control in the region such that the equilibrium of the linear subsystem is reached in a finite time whose value is tunable by parameter setting of the TSMs. The finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point. Chattering phenomenon commonly associated with sliding mode control does not occur.