This paper proposes a new approach for stabilizing a homogeneous solution in reaction-convection-diffusion system with oscillatory kinetics, in which moving or stationary patterns emerge in the absence of control. Specifically, we aim to suppress patterns by using a spatially weighted finite-dimensional feedback control that assures stability of the solution according to Lyapunov's direct method. A practical design procedure, based on spectral representation of the system and dissipative nature of parabolic PDEs, is presented.
- Distributed control
- Lyapunov's direct method
- Nonlinear partial differential equations
- Sector nonlinearity
- Wave suppress