ℓ1-to-ℓ1 interval observation design for discrete-time switched linear systems under dwell time constraint

Xiaozeng Xu, Yang Li, Can Liu and Hongbin Zhang

International Journal of Systems Science, 2020, vol. 51, issue 4, 759-770

Abstract: In this brief article, sufficient conditions characterising the $\ell _1 $ℓ1-gain of discrete-time switched positive linear systems (DSPLSs) under dwell time constraint are obtained. The dwell time refers to range, minimum and constant dwell time. These conditions are presented in terms of linear programming. Then, convex sufficient conditions on the existence of $\ell _1 $ℓ1-to- $\ell _1 $ℓ1 interval observers for discrete-time switched linear systems (DSLSs) are derived based on the $\ell _1 $ℓ1-gain stability analysis results of DSPLSs. By adding some parameter matrices, the proposed interval observer has a new structure that relaxes the design conditions. Suitable observer gains can be extracted from the solution of the dimensional optimisation problem where the $\ell _1 $ℓ1-gain of the system mapping the disturbances to the weighted observation errors is minimised. At last, some numerical examples of DSLSs are given for illustration.

Date: 2020
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DOI: 10.1080/00207721.2020.1740822

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