Conditions for annular finite‐time stability of Itô stochastic linear time‐varing systems with Markov switching

Abstract

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 Ito 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.