Abstract
This paper considers the problem of simultaneous stabilization, tracking, and disturbance rejection (SSTDR) of a set of linear time-invariant, single-input single-output plants. Necessary and sufficient conditions for being able to solve this problem are developed. These conditions involve the satisfaction of a number of equations in some rational functions related to the coprime factorization of the given plants. It is shown that the N-plant SSTDR problem is equivalent to simultaneously stabilizing a related set of N - 1 plants using a stable controller, and that under an additional simple condition the N-plant SSTDR is also equivalent to the simultaneous stabilization of a related set of N - 2 plants by a stable controller having a stable inverse. In addition, it is shown that under certain conditions a controller that solves the SSTDR problem can be easily obtained. Finally, a computationally tractable method is developed for obtaining the parametrized controllers for the solution of the general two-plant SSTDR problem.
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