Set-Based State Estimation For Discrete-Time Semi-Markov Jump Linear Systems Using Zonotopes

This paper is dedicated to the set-based state estimation problem of discrete-time semi-Markov jump linear systems via using zonotopes. By performing a consistency test regarding the system plant and measurement outputs, an intersected zonotope is established on the basis of a correction matrix. With the discrete-time semi-Markov kernel and$P$-radius concepts, the boundedness and$L_{\infty }$performance analysis are addressed for the underlying systems under the influence of unknown-but-bounded uncertainties. Subsequently, the numerically testable conditions are developed to obtain the optimal correction matrices. Then a zonotope-based outer approximation can be derived for the accurate state set. Finally, a case study on a vertical take-off and landing helicopter as well as a numerical example is considered to show the usefulness of the proposed results.