Abstract
The problem of robust H∞ control is investigated for Markov jump systems with nonlinear noise intensity function and uncertain transition rates. A robust H∞ performance criterion is developed for the given systems for the first time. Based on the developed performance criterion, the desired H∞ state-feedback controller is also designed, which guarantees the robust H∞ performance of the closed-loop system. All the conditions are in terms of linear matrix inequalities (LMIs), and hence they can be readily solved by any LMI solver. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methods.
Highlights
Many dynamical systems are subject to random abrupt changes, which may be caused by random failures and repairs of the components, changes in the interconnections of subsystems, sudden environment changes, etc
The obtained controller design method only needs to solve a set of pure linear matrix inequalities (LMIs) rather than nonlinear matrix inequalities (NLMIs), which can be readily solved by any LMI solver
As shown in section, the obtained controller design method only involves a set of pure LMIs rather than NLMIs, which can be readily solved by any LMI solver
Summary
Many dynamical systems are subject to random abrupt changes, which may be caused by random failures and repairs of the components, changes in the interconnections of subsystems, sudden environment changes, etc. The proposed controller design methods in both [16] and [17] need to solve a set of nonlinear matrix inequalities (NLMIs) Such NLMIs cannot still be completely solved up to now [18]. To the author’s best knowledge, the problem of H∞ control for MJSs with nonlinear noise intensity function and uncertain transition rates has not been fully investigated. This paper is concerned with the robust H∞ control for MJSs with nonlinear noise intensity function and uncertain transition rates. If their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations
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