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January 24, 2026

Exact observability of semi‐Markov jump stochastic systems

FSFangxu SuShandong University of Science and Technology DWDong WangShandong University of Science and Technology WZWeihai ZhangShandong University of Science and Technology

Key Points

The central aim is to explore the exact observability of semi-Markov jump stochastic systems using new criteria.
Introduced an extended system method for observability analysis in semi-Markov jump stochastic systems.
Transformed observability analysis into several extended systems in the moment sense.
Derived the Popov-Belevith-Hautus criterion and rank criterion for observability.
Identified exact criteria for observability in the moment sense for the first time.
Illustrated the effectiveness of the proposed methods with an example.

Abstract

Abstract This paper focuses on the exact observability of semi‐Markov jump stochastic systems (s‐MJSSs). An extended system method (ESM) for s‐MJSSs is introduced to transform the observability analysis for s‐MJSSs in the th moment sense into several extended systems. By applying the ESM, the Popov‐Belevith‐Hautus (PBH) criterion and the rank criterion for exact observability in the th moment sense are derived for the first time. Additionally, the example is provided to illustrate the effectiveness of the proposed conclusions.

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