Robust ℒ₂ disturbance attenuation for a class of uncertain Lipschitz nonlinear systems with input delay

ABSTRACT

In this paper, we study a robust ${\mathcal{L}}_2$ disturbance attenuation problem that arises when applying the Artstein–Kwon–Pearson reduction transformation for a class of uncertain Lipschitz nonlinear systems with input delay and external disturbances. A conventional predictor-based feedback controller is adopted with the control gain matrix carefully identified by solving a couple of sufficient conditions in terms of linear matrix inequalities . Lyapunov–Krasovskii functionals are constructed to guarantee that the robust ${\mathcal{L}}_2$ disturbance attenuation problem can be solved by the proposed controller. A numerical example is included to validate the performance of the proposed controller.

KEYWORDS:

• Disturbance attenuation
• input delay
• Lipschitz nonlinearity
• parametric uncertainty
• robust stabilisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61673034 and 61573143] and Science and Technology Facilities Council (STFC) under Newton Fund with grant number ST/N006852/1.