Strong practical stability and stabilization of 2D differential-discrete linear systems

This paper considers two-dimensional (2D) differential linear systems recursive over the upper right quadrant described by well known state-space models. Included are differential linear repetitive processes which evolve over a subset of the upper right quadrant of the 2D plane. In particular, information propagation in one direction only occurs over a finite duration and is governed by a matrix differential linear equation. A stability theory exists for these processes but there has also been work which has led to the assertion that this is too strong in many cases of applications interest. This paper develops strong practical stability for differential linear repetitive processes as a possible alternative in such cases. Also stabilizing control law design algorithms are developed as the first step towards applying this new stability analysis to physical examples.