Robust Stabilization of the Generalized Triangular Form Nonlinear Systems With Disturbances

We investigate the problem of global uniform input-to-state stabilization of nonlinear generalized triangular form (GTF) control systems of ODE with time-varying and periodic dynamics and with external essentially bounded disturbances. Our first main result is a statement which is a kind of extension of theorems on “adding an integrator” to the case of input-to-state stabilization of GTF systems. As a corollary we immediately obtain our second main result on global uniform input-to-state stabilzation of GTF systems w.r.t. the external disturbances. The latter is a generalization of the recent result, devoted to the global asymptotic stabilization of the GTF systems without disturbances. It is essential that the proof of the main result is based on the converse ISS Lyapunov theorems for the time-varying systems, which allows to simplify construction proposed our recent work.