Higher order sliding-mode observers with scaled dissipative stabilisers

ABSTRACT

This paper proposes a global theoretically exact finite-time convergent observer for a class of nonlinear systems, which are not necessarily bounded-input-bounded-state with respect to the unknown inputs. With this aim, a scaled dissipative stabiliser is suggested ensuring that the highest derivative of the output estimation error is independent from the stabiliser gains. After this, a higher order sliding-mode differentiator with the gains adjusted to the upper bound of the unknown inputs is applied achieving finite-time convergence.

KEYWORDS:

• Sliding-mode observer
• dissipative observer
• nonlinear systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Solutions of differential equations with discontinuous right-hand sides will be understood in Filippov's sense (Filippov, 2013).

2. (⋆) indicates that the matrix is a symmetric matrix.

Additional information

Funding

The study was supported by CONACyT (Consejo Nacional de Ciencia y Tecnología) [grant number CVU 419644]; PAPIIT-UNAM (Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica) [IN 113216]; Fondo de Colaboración del II-FI UNAM [INGSBAS-100-2015].