Open AccessConditions for annular finite‐time stability of Itô stochastic linear time‐varing systems with Markov switching
Author(s) -
Tartaglione Gaetano,
Ariola Marco,
Amato Francesco
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0633
Subject(s) - control theory (sociology) , markov chain , stability (learning theory) , linear system , markov process , context (archaeology) , computer science , mathematics , mathematical optimization , control (management) , machine learning , artificial intelligence , mathematical analysis , paleontology , statistics , biology
In this study, the authors tackle some control problems related to the class of continuous‐time, stochastic linear time‐varying systems with Markov switching. First, the annular stochastic finite‐time stability problem is considered, and two sufficient conditions are derived by considering the Itô formalism. Both conditions require the solution of a feasibility problem based on differential linear matrix inequalities. The former turns out to be less conservative and, therefore, is exploited in the analysis context; however, it cannot be converted into a computationally tractable condition for feedback purposes. The latter, which is based on a more conservative assumption, allows us to solve the state‐feedback design problem. They show that the proposed approach obtains less conservative results with respect to the previous literature. Moreover, the application of the methodology to the finite‐time control of a satellite illustrates the effectiveness of the proposed approach when facing engineering problems.