Uniform output regulation via approximated input–output linearisation for lightly damped internal dynamics

Abstract

We present a general framework for the design of a damping controller to tame lightly damped internal dynamics and to assess the stability of an approximate input–output linearised closed-loop system. In nonlinear systems, conclusions cannot be drawn regarding the stability of internal dynamics even though the zero dynamics is globally stable. Here, we investigated the sufficient conditions with a parameter-dependent Lyapunov (PDL) function for semi-globally exponential stability of damped internal dynamics. Using a composite Lyapunov function based on the PDL function, the uniform boundedness of the output regulation error is established within a region of interest. Controllability and observability analyses offer a theoretical guideline as to how a damping controller can be designed in the view of control effort and transient performance.

Keywords:

• input–output feedback linearisation
• damping control
• stability of nonlinear system
• internal (zero) dynamics

Acknowledgements

This work was supported by the Power Generation and Electricity Delivery of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Ministry of Knowledge Economy, Republic of Korea (No. 2010T100100346). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0000891).