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Stability of linear stochastic delay differential equations with infinite Markovian switchings
Author(s) -
Song Ruili,
Zhu Quanxin
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3905
Subject(s) - exponential stability , mathematics , equivalence (formal languages) , mean square , stability (learning theory) , exponential function , differential equation , mathematical analysis , nonlinear system , pure mathematics , computer science , physics , machine learning , quantum mechanics
Summary This paper investigates the stability of linear stochastic delay differential equations with infinite Markovian switchings. Some novel exponential stability criteria are first established based on the generalized It ô formula and linear matrix inequalities. Then, a new sufficient condition is proposed for the equivalence of 4 stability definitions, namely, asymptotic mean square stability, stochastic stability, exponential mean square stability with conditioning, and exponential mean square stability. In particular, our results generalize and improve some of the previous results. Finally, two examples are given to illustrate the effectiveness of the proposed results.