Stability and Stabilization of Delayed Fuzzy Semi-Markov Jump Systems with Incomplete Transition Rates and Quadratic Fuzzy Lyapunov Matrix via Quantized Control Design

Abstract

This study examines the stability and stabilization issues of a type of state-quantized, time-varying delayed (TVD) Takagi–Sugeno (T–S) fuzzy semi-Markov jump systems. First of all, in order to obtain more information of T–S fuzzy systems, an augmented fuzzy Lyapunov–Krasovskii Functional (LKF) is formatted including a quadratic fuzzy Lyapunov matrix (QFLM). In addition, a novel quadratic polynomial inequality (QPI) is applied to narrow the estimation gap for TVD and a quantized controller is used to reduce control accuracy. Then, the sufficient conditions for system stability and stabilization via quantized controller are attained on the basis of Lyapunov stability theory and linear matrix inequalities method. Finally, three examples show how the constructed controller can successfully regulate the examined system and the proposed technique is less conservative than those of the former ones.