H   ∞   state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems | Zendy

Ding Yucai | Zendy; Liu Hui | Zendy; Shi Kaibo | Zendy

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H ∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems

Author(s) -

Ding Yucai,

Liu Hui,

Shi Kaibo

Publication year - 2016

Publication title -

optimal control applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.458

H-Index - 44

eISSN - 1099-1514

pISSN - 0143-2087

DOI - 10.1002/oca.2245

Subject(s) - mathematics , state transition matrix , control theory (sociology) , lyapunov function , linear matrix inequality , transition rate matrix , matrix (chemical analysis) , bounded function , controller (irrigation) , state (computer science) , convex combination , convex optimization , regular polygon , symmetric matrix , mathematical optimization , mathematical analysis , computer science , nonlinear system , eigenvalues and eigenvectors , control (management) , algorithm , materials science , artificial intelligence , composite material , biology , geometry , quantum mechanics , agronomy , physics , statistics

Summary This paper studies the problem of H ∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems. The time‐varying transition rate matrix in continuous‐time domain is considered to lie in a convex bounded domain of polytopic type. By constructing a parameter‐dependent Lyapunov function and fully considering the information about the rate of change of time‐varying parameters, a new sufficient condition on the existence of an H ∞ state‐feedback controller is provided in the form of a parameter‐dependent matrix inequality. Moreover, based on the structure characteristics of Lyapunov matrix and transition matrix, the parameter‐dependent matrix inequality is converted into a finite set of linear matrix inequalities, which can be readily solved. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

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