Input-to-state stabilization of the perturbed systems in the generalized triangular form

TL;DR

This paper develops a feedback control strategy for nonlinear systems in generalized triangular form, ensuring global input-to-state stability despite time-varying and periodic disturbances.

Contribution

It combines existing stabilization methods with ISS theory to achieve semi-uniform input-to-state stability for GTF systems with disturbances.

Findings

Constructed a feedback controller ensuring global stability.

Achieved semi-uniform input-to-state stability.

Extended stabilization techniques to systems with external disturbances.

Abstract

We consider nonlinear control systems of the so-called generalized triangular form (GTF) with time-varying and periodic dynamics which linearly depends on some external disturbances. Our purpose is to construct a feedback controller which provides the global input-to-state stability of the corresponding closed-loop w.r.t. the disturbances. To do this, we combine the method proposed in the earlier work \cite{pavlichkov_ge_2009} devoted the the global asymptotic stabilization of the GTF systems without disturbances with the ISS theory for time-varying systems proposed in \cite{wang}. Following this pattern we construct a feedback which provides the properties of uniform global stability and asymptotic gain w.r.t the disturbances. Then we obtain the semi-uniform ISS of the closed-loop system.