Less Conservative Aperiodic Sampled-Data Control Design for Takagi–Sugeno Fuzzy Systems via a Novel Non-Quadratic Looped-Functional

Abstract

This paper addresses the design of an aperiodic sampled-data controller for Takagi-Sugeno (T-S) fuzzy systems. To achieve a larger maximum allowable transfer interval (MATI) between consecutive sampling instants, less conservative stability conditions are derived by constructing an improved Lyapunov functional. The proposed method introduces new formulations based on the integral of membership functions over the sampling interval, resulting in Lyapunov functionals with non-quadratic structures. In particular, a two-sided looped functional and a discontinuous functional are developed, both dependent on the membership functions and the aperiodic sampling interval. These formulations generalize the existing quadratic-type functionals in the literature, thereby significantly reducing conservatism. Moreover, unlike some existing membership-function-dependent Lyapunov functionals, the proposed approach does not require the derivatives of the membership functions, which typically restrict stability analysis to local sectors. The effectiveness of the proposed method is verified through numerical simulations and a practical example. Note to Practitioners—In many digital control applications, practitioners must balance performance with constraints such as energy usage, communication load, and limited sampling resources. For nonlinear systems represented through fuzzy T-S models, existing sampled-data control methods often impose conservative sampling requirements because they do not fully exploit the available membership-function information. The proposed approach alleviates these limitations by incorporating membership-function-dependent terms in the Lyapunov functional construction, offering greater flexibility and reduced conservatism. This framework can also be adapted to recent looped-functional developments for further performance gains. Numerical examples and a stirred tank reactor system demonstrate the effectiveness and practical advantages of the proposed conditions over other recent methods, confirming their relevance for engineering applications.