Practical Stabilization of Networked Takagi-Sugeno Fuzzy Systems via Improved Jensen Inequalities

This work addresses the problem of aperiodically sampled control for the networked Takagi-Sugeno (T-S) fuzzy systems, where the aperiodically sampled input is generated by a periodic sampler and an event-triggered mechanism (ETM). The purpose of ETM is used to reduce the computational and communication burdens. For guaranteeing controller robustness, the practical stability of T-S fuzzy systems is considered by using the Lyapunov method and linear matrix inequality (LMI) technique. As one of the most powerful inequalities for deriving stability criteria using LMIs, Jensen's inequality has recently been improved by various authors for the stability analysis of delayed systems. However, these results are conservative to obtain lower bounds for integrals with an exponential term. Inspired by this, improved integral inequalities are derived in this work, and they are applied to obtain practical stability criteria for aperiodically sampled control. Finally, a numerical example on flight control of a helicopter is given to illustrate the effectiveness of the obtained practical stability criteria. Furthermore, the effectiveness of the improved Jensen inequalities on the exponential stability criteria is illustrated by numerical comparisons.