This paper investigates a mixed H2/Passivity performance control problem of uncertain stochastic systems. Based on Itô stochastic equation, the considered system is described by a linear difference equation with multiplicative noise term. To minimize output energy and guarantee asymptotical stability, the H2 scheme is employed. Moreover, passivity theory is applied to constrain the effect of external disturbance on the system. According to the passivity theory, a general and flexible mixed performance controller design method is proposed. Based on Lyapunov function, some sufficient conditions are derived into extended Linear Matrix Inequality (LMI) form which reduces conservatism of finding the feasible solutions. Furthermore, the derived conditions can be directly solved by convex optimization algorithm to establish a controller such that asymptotical stability and mixed H2/Passivity performance of the uncertain stochastic system are achieved. At last, an inverted pendulum system is used to show effectiveness and applicability of the proposed method.
Ku, Cheung-Chieh; Chen, Rui-Wen; Chen, Guan-Wei; and Chang, Wen-Jer
"ROBUST CONTROL OF DISCRETE-TIME UNCERTAIN STOCHASTIC SYSTEMS SUBJECT TO MIXED H2/PASSIVITY PERFORMANCE,"
Journal of Marine Science and Technology: Vol. 26:
5, Article 4.
Available at: https://jmstt.ntou.edu.tw/journal/vol26/iss5/4