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Mathematical Problems in Engineering
Volume 2015, Article ID 831576, 8 pages
Research Article

Stability Criterion of Linear Stochastic Systems Subject to Mixed /Passivity Performance

Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Received 19 September 2014; Accepted 5 January 2015

Academic Editor: Xinzhu Meng

Copyright © 2015 Cheung-Chieh Ku et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI) form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.