Exact observability of semi‐Markov jump stochastic systems

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.