Switching Control of 2-D Kuramoto-Sivashinsky Equation under Averaged Measurements

This paper deals with the switching control design of Kuramoto-Sivashinsky equation (KSE) in two-dimensional (2-D) rectangular domain
$\Omega$
. It is supposed that
$\Omega$
is divided into
$N$
subdomains and the discrete-time averaged measurements are available. Under the distributed sensors and actuators in space, the stabilization of 2-D KSE by switching is studied where only one pair of actuator and sensor is active during a certain interval of time (or only one pair of actuator and sensor is employed to move in the spatial domain). In the latter case, the moving time of actuator-sensor pair is considered as an additional switching between the open-loop system and the closed-loop switched system. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) to ensure regional stability of the closed-loop system.