Impulsive observer-based admissibilization for delayed degenerate jump systems and application to DCM-IP device

Abstract

This paper researches the impulsive observer-based admissibilization for delayed degenerate Markovian jump systems with completely known or partly unknown transition rates. In contrast with the normal continuous-time observer, the advantage of the impulsive observer is that it uses only the measurement outputs at the impulses moments to estimate the states of the controlled system. In order to make the obtained results more universalist, a novel piecewise differentiable Lyapunov–Krasovskii functional with piecewise linear impulse auxiliary functions is established, which can grasp the mixed characteristics of impulses instants information and Markovian jumping modes information. At the same time, singular value decomposition (SVD) technology is used to surmount the influence of the internal impulses of the degenerate system. Improved sufficient conditions about stochastic admissibilization for delayed degenerate impulsive Markovian jump systems are obtained in the form of linear matrix inequalities (LMIs) via mode-dependent impulsive observer-based state feedback controller. Direct current motor-controlled inverted pendulum (DCM-IP) device and a numerical example are utilized to verify the validity and practicability of the results acquired in this paper.