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Event-triggered $$H_{\infty}$$ control for a class of nonlinear networked control systems using novel integral inequalities. (English) Zbl 1356.93058
Summary: This paper is concerned with event-triggered $$H_{\infty}$$ control for a class of nonlinear networked control systems. An event-triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event-triggered transmission scheme, the closed-loop system is modeled as a system with an interval time-varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov-Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event-triggered $$H_{\infty}$$ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality-based conditions are formulated to design both event-triggered and time-triggered $$H_{\infty}$$ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

##### MSC:
 93C65 Discrete event control/observation systems 93B36 $$H^\infty$$-control 93C10 Nonlinear systems in control theory 93C57 Sampled-data control/observation systems 93D21 Adaptive or robust stabilization 93C15 Control/observation systems governed by ordinary differential equations 93B52 Feedback control
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