Understandings of incremental backstepping controller considering measurement delay with model uncertainty

In this paper, closed loop characteristics with an incremental backstepping (IBKS) controller are investigated with consideration of measurement delays and model uncertainties. To judge absolute stability of the system, a systematic analysis framework is proposed which examines the existence of unstable poles from a derived characteristic equation with high nonlinearity due to the considered measurement delays. One of the key findings from the analysis results is that the system is stable only when a specific relationship between the measurement delays is satisfied and this stability condition is affected by the model uncertainty. Critical understandings about individual and integrated effects of the measurement delays and the model uncertainties to the system are suggested through a comparative study. Verification and validation of the obtained properties from the framework are performed through simulations.