Observer for Nonlinear Systems with Time-Varying Delays: Application to a Two-Degrees-of-Freedom Helicopter

Abstract

This paper deals with the problem of the estimation of non-uniformly nonlinear systems with time-varying delays in the state and input. In addition, the problem of the sampled output measurement is also been addressed. Thus, an observer design for a class of uncertain, non-uniformly nonlinear systems in the presence of time-varying delay is proposed. A continuous–discrete observer based on a high-gain approach is designed to achieve undelayed estimation. Thus, sufficient conditions to ensure the convergence of the observer are obtained. The analysis is based on a Lyapunov–Krasovskii functional, which shows that the bounded observation error depends on the sizes of the known upper delay and the upper sampling rate. The performance of the proposed algorithm is evaluated by considering a control-based observer for a two-degrees-of-freedom helicopter system with a known time-varying delay and sampled output measurements.

Keywords

• observer synthesis
• nonlinear system
• uncertain system
• sampled system
• time-varying delays