| Summary: | This paper focuses on the problem of finite-time <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> static output feedback control for <inline-formula><math display="inline"><semantics><mrow><mi>I</mi><mi>t</mi><mover accent="true"><mi>o</mi><mo>^</mo></mover></mrow></semantics></math></inline-formula> stochastic systems with Markovian jumps (MJs). First of all, by introducing a new state vector and a novel signal, several sufficient conditions for the existence of static output feedback controllers are established for the considered systems with completely known transition rates (CKTRs) and partially known transition rates (PKTRs), respectively. Then the static output feedback controllers are designed via solving linear matrix inequalities (LMIs), which ensure the closed-loop systems are stochastic <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> finite-time boundedness. The validity of the developed method was demonstrated through two examples.
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