Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré–Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.