Dissipativity‐Oriented Event‐Triggered Sliding Mode Control for Semi‐Markovian Jump PDE Systems Against Periodic DoS Attacks

The primary aim of this work is to explore the exponential stabilization of semi‐Markovian jump partial differential equation systems with Neumann boundary conditions by making use of a security‐based resilient event‐triggered sliding mode controller. To accurately reflect reality, the system under investigation is exposed to generally uncertain transition rates, periodic denial‐of‐service attacks, and randomly occurring linear fractional uncertainties. Specifically, an event‐triggered protocol is put forward to curtail the transmission of nonessential data, thereby improving the network's effectiveness. Moreover, to ensure the system remains robust against potential threats, the controller design takes random gain fluctuations as well as periodic denial‐of‐service jamming attacks. Additionally, the linear fractional uncertainties and gain fluctuations are modeled using a Bernoulli distribution. Following this, an integral sliding surface is formulated with the aid of sliding mode theory, after which a sliding mode controller incorporating a security‐based resilient event‐triggered protocol is designed. Moreover, the effect of external disturbances is minimized through the implementation of extended dissipativity performance. Thereupon, with the application of Lyapunov stability theory and some integral inequalities, the conditions for the global exponential stabilization of the considered system are achieved in the context of the linear matrix inequalities. Lastly, the effectiveness and practical applicability of the developed control strategy are validated with the help of two numerical examples.