State observers for mechanical systems with unilateral constraints : a discretization-based approach and experimental analysis

Abstract

This monograph deals with the state observer design for mechanical systems with unilateral constraints. After the mathematical modeling is discussed in detail, necessary tools, which extend Lyapunov stability theory, are provided. A state observer design approach is investigated, which, in contrast to most existing observer designs, does not assume that closed contacts are instantaneously detected through measurements. In particular, a time discretization-based method is analyzed, which allows to circumvent some of the main difficulties caused by discontinuous time evolutions. Moreover, various state observer designs are implemented and tested on an experimental setup consisting of an impact oscillator.