Stability Analysis for a Class of Linear $2\times 2$ Hyperbolic PDEs Using a Backstepping Transform
Journal: IEEE Transactions on Automatic Control
Year: 2019

In this paper, we develop a sufficient stability condition for a class of coupled first-order linear hyperbolic partial differential equations (PDEs) with constant coefficients that appear when considering target systems for backstepping boundary control.Using a backstepping transform, the problem is reformulated as a stability problem for a difference equation with distributed delay. Finding the explicit solution to the backstepping kernels, we derive an explicit sufficient condition depending