Direct Lyapunov method for hyperbolic systems on the plane with time-periodic coefficients

In the framework of the direct Lyapunov method, we establish tests for the exponential stability of solutions of boundary value problems (the mixed problem and the Cauchy problem for hyperbolic systems of the class in question) in the L ₂-norm. In these tests, the conditions on the derivative of the Lyapunov functional along the trajectories of the system are weakened compared with the known results for the case of any smooth coefficients. The main result is illustrated by the example of the mixed problem for the telegraph system with small friction periodically switched on.