Stabilization of Fuzzy Hydraulic Turbine Governing System With Parametric Uncertainty and Membership Function Dependent <italic>H</italic>&#x221E; Performance

Abstract

This paper examines the stabilization problem and membership function dependent $H_\infty $ performance analysis for uncertain hydraulic turbine governing systems with stochastic actuator faults and time-varying delays via sampled-data control. At first, the nonlinear hydraulic turbine systems are modeled as Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and bounded external disturbance through membership functions. Then, a novel delay-dependent looped Lyapunov-Krasovskii functional (LKF) is formulated with complete information throughout the sampling interval. In the meantime, a membership function dependent $H_\infty $ performance index is suggested to diminish the impact of disturbances on the uncertain fuzzy system. Based on the robust control and novel LKF, new delay-dependent stability conditions for the closed-loop system are attained in the framework of linear matrix inequalities (LMIs). At last, the numerical example validates the proposed theoretical contributions in terms of achieving robust stability and minimizing disturbance attenuation levels.

Keywords

• Hydraulic turbine governing system
• linear matrix inequality
• sampled-data control
• stochastic actuator fault
• T-S fuzzy model