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On the order of simultaneously stabilizing compensators

O. Toker
1996 IEEE Transactions on Automatic Control  
In this paper, simultaneous strong stabilization problem is considered and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator, in terms of the plant orders. A similar problem was also considered in [lo], where it was shown that such a bound does not exist for the strong stabilization problem of a single plant. But the examples given in [lo] were forcing an approximate unstable pole-zero cancellation, or forcing the distance
more » ... the distance between two distinct unstable zeros to go zero. In this paper it is shown that: (i) if approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeros are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator; (ii) and for the simultaneous strong stabilization problem (even for the two plant case), such a bound cannot be found.
doi:10.1109/9.486644 fatcat:ot334vzgdnb7vgnmkbwhslsaci