Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

Abstract

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.

Keywords:

• nonlinear systems
• finite-time stabilisation
• output feedback

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (61104068), Natural Science Foundation of Jiangsu Province (BK2010200), Research Fund for the Doctoral Program of Higher Education of China (20090092120027, 20110092110021) and China Postdoctoral Science Foundation Funded Project (2012M511176).

Notes

Notes

1. For simplicity, in this article we assume with an even integer q and an odd integer p. Based on this, r _i  = 1 + (i − 1)τ, i = 1, … , n + 1, will be odd in both the denominator and numerator. Note that an equivalent result can be achieved for a real number τ.

2. In general, . For simplicity, we can work with instead of V to obtain the inequality (15).