ABSTRACT
A systematic method for the design of the H2 controller for two-dimensional (2-D) systems in terms of linear matrix inequality has been developed. The developed 2-D H2 control design method is of great importance to those systems that have 2-D behavior and can be modeled using 2-D linear system models. This chapter provides 2-D controllers in stabilization and error minimization of systems that have 2-D behavior and can be modeled as a 2-D model. In self-servo track writing, track shape errors such as non-circularity are introduced by mechanical disturbances, spindle motor vibration and other factors when writing the propagation tracks. The typical closed-loop transfer function will amplify the error at the frequency where its magnitude is more than 0 dB. The target of error propagation containment is to reject the written-in error due to track non-circularity recorded in propagated tracks so that the circular concentric tracks are achieved in every propagation trace.
