Absolute stability of coupled dissipative parabolic equations with wave-speed mistuning

Recent work has focussed on the stabilizing properties of symmetry-breaking in oscillator systems. We consider the problem of achieving global absolute stability of an unstable equilibrium solution of coupled dissipative parabolic equations with non-homogeneous coefficients. In particular, we consider the stabilization of a PDE model describing thermo-acoustic instabilities with wave-speed mistuning. Sufficient conditions for absolute stability of the infinite-dimensional system are established by the feasibility of two finite-dimensional linear matrix inequalities (LMI). Numerical results are presented for an example problem.