Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.

KEYWORDS:

• Time-varying delay
• nonlinear systems
• output feedback
• robust control
• linear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

R. Sanz  http://orcid.org/0000-0001-8581-2742

P. García  http://orcid.org/0000-0002-1202-1269

E. Fridman  http://orcid.org/0000-0002-8773-9494

P. Albertos  http://orcid.org/0000-0002-7277-5927

Notes

1 The equality $z_{j-1}(t-h_j)-\overline{z}(t-h/m-h_j)={\tilde{z}}_j(t-h/m)-{\tilde{z}}_{j-1}(t-h/m)$ was used to derive (12(12) $\begin{array}{rl}{\dot{\tilde{z}}}_j\left(t\right)& =A_z{\tilde{z}}_j\left(t\right)-L_j{\tilde{z}}_j\left(t-\frac{h}{m}\right)+L_j{\tilde{z}}_{j-1}(t-\frac{h}{m})\\ & -B_z\mathcal{I}\left(\dot{u}\right)+B_z\delta g_j,\end{array}$(12) ), which can be obtained by subtracting ${\tilde{z}}_j\left(t\right)$ and ${\tilde{z}}_{j-1}\left(t\right)$ as defined in (10(10) ${\tilde{z}}_j\left(t\right)=z\left(t\right)-{\overline{z}}_j(t-h_j),$(10) ), delaying the resulting expression by h/m units of time, and using the fact that $h_{j-1}+h/m=h_j$.

Additional information

Funding

This work was partially supported by: Ministerio de Economía y Competitividad, Spain (TIN2017-86520-C3-1-R); Universitat Politècnica de València (FPI-UPV 2014 PhD Grant); and Israel Science Foundation (Grant No. 1128/14).