Observer-based finite time H_∞ control of nonlinear discrete time-varying systems with an adaptive event-triggered Mechanism

The problem of finite time stability and synthesis is discussed for nonlinear discrete time-varying systems by using the T-S fuzzy model. To reduce the communication network resources, two adaptive event-triggered mechanisms (AETMs) are taken into consideration in sensor-to-observer (S/O) and observer-to-controller (O/C) channels. The thresholds of the AETMs are adjusted according to the estimation error rather than some fixed ones. Sufficient conditions for developing an observer-based time-varying control are obtained, which ensure the time-varying error system to be finite time stable and satisfy the H_∞ performance simultaneously. Moreover, using the singular value decomposition technique, recursive linear matrix inequalities conditions are obtained for computing the gains of the controller and observer. Finally, the superiority and applicability of the proposed method are demonstrated by examples.