© The Institution of Engineering and Technology
This study is concerned about the quantitative exponential stability (QES) and stabilisation of discretetime Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finitetime stability (GFTS), the relations among QES, GFTS and finitetime stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observerbased controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results.
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