Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

A note on the genericity of simultaneous stabilizability and pole assignability

“…The results in the first and third category are already known [5], but the present proofs are simpler. The result concerning simultaneous strong stabilizability is new, and as far as we are able to determine, cannot be derived using the methods of [5]. In addition, we.have presented some lemmas concerning generic greatest common divisors which may be of some independent interest.…”

“…In [4] it was shown that two plants P 1 ,P2, each having dimension I Xm, are generically simultaneously stabilizable if max{1,m}>1. This result was extended in [5], where it was shown that a collection of plants Pl, ... ,P,, each having dimenison lXm, is generically simultaneously stabilizable if max{l,m})r. In the present note, a simple proof is given of this last result, and it is also shown that generic strong simultaneous stabilizability holds if max{l,m}>r; this is a new result.…”

“…A precise definition is given in Section 5. The only results concerning this property are in [5], where it is shown that generic pole assignability holds if max{l,m})r, and in addition, an estimate is given of the dynamic order of a controller that achieves it. In the present note, we give a simple proof of this result as well.…”

“…In this section, we give a simple proof of a result from [5] concerning generic simultaneous pole assignability. In order to prove the main result, it is necessasry first to define the concept of characteristic polynomials.…”

Stabilization of Linear Systems

“…The simultaneous control problem has attracted many researchers over the last many years. Some of the results for single-input single-output (SISO) transfer functions were reported in [6,7]. Peterson [8] obtained a nonlinear state feedback controller that quadratically stabilized a set of single-input linear systems simultaneously.…”