Fractional Exponent-Based Looped-Lyapunov Functional for Mode-Dependent Sampled-Data Control of T–S Fuzzy Markovian Jump Systems With H_∞ Performance

In this article, a novel fractional exponent (FE)-based looped-Lyapunov functional (FEBLLF) is proposed to analyze the stochastic stability (SS) criteria of a nonlinear Markovian jump systems (MJSs) under a mode-dependent sampled-data control through the Takagi–Sugeno (T–S) fuzzy approach. An FE, represented by an exponential function with a fractional parameter, is introduced to define looped FEs (LFEs) These LFEs are utilized to construct a novel FEBLLF and to partition the sampling interval into four distinct sampling subintervals, providing detailed information about the state within each subinterval. Subsequently, the sampling-dependent sufficient conditions are obtained as linear matrix inequalities to ensure the SS of the T–S fuzzy MJSs with H_∞ performance level \upgamma and to verify the effectiveness of the proposed results, a nonlinear mass–spring system is assessed. In addition, comparative examples are discussed to illustrate the better conservative results of the proposed approaches.