H_∞ fuzzy intermittent boundary control for nonlinear parabolic distributed parameter systems

For nonlinear space-varying parabolic distributed parameter systems, this paper introduces an H_∞ fuzzy intermittent boundary control, where the output measurements are only available at some specified boundary position (i.e., boundary measurements). Initially, a Takagi–Sugeno fuzzy parabolic partial differential equation is used to precisely describe the nonlinear space-varying parabolic distributed parameter system. Then, under boundary measurements, an H_∞ fuzzy intermittent boundary control design based on the Takagi–Sugeno fuzzy parabolic partial differential equation model ensuring the exponential stability with an H_∞ performance for closed-loop space-varying distributed parameter system is subsequently obtained via spatial linear matrix inequalities by employing inequality techniques and piecewise switching-time-dependent Lyapunov function. Furthermore, in order to solve the H_∞ fuzzy intermittent boundary controller design of nonlinear space-varying parabolic distributed parameter systems under boundary measurements, we express spatial linear matrix inequalities as linear matrix inequalities and further present some linear matrix inequality based fuzzy intermittent boundary control design conditions respecting the property of membership functions. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed H_∞ fuzzy intermittent boundary control method.