Feedback system design: The single-variate case — Part II

Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

“…As a further corollary, we obtain one of the results obtained by Saeks and Murray in [14] (see also [15]): Corollary 1.7. (Saeks-Murray [14]).…”

“…As pointed out in [15], this question arises in reliability theory, where G 2 (s), --9 G r (s) represent a plant G x (s) operating in various modes of failure, and K(s) is a nonswitching stabilizing compensator. Of course, for the same reason, it is important in the stability analysis and design of a plant which can be switched into various operating modes.…”

Simultaneous stabilization of full state information Linear Time‐Invariant systems

“…The Simultaneous Stabilization (SS) problem is to design K 0 ( s ) stabilizing l plants that is equivalent to stabilize l − 1 plants as shown by 1 using a common stable controller. In particular, a result of 1 states that if P 0 ( s ) is stable and P 1 ( s ) is arbitrary, then P 0 ( s ) and P 1 ( s ) can be simultaneously stabilized ⟺ P 1 ( s ) − P 0 ( s ) is strongly stabilizable, as proposed by 4, 5 (see the books of 2, 3). Conditions for SS are given by 4, 5 (see Lemma 16 and Theorem 22 in Section 5.4 of 3), based on left and right coprime factorizations over ℜℋ ∞ (l.c.f.…”

“…states that the number of poles between any pair of real and unstable McMillan zeros is even. Also, the SS of a given family of linearplants has been solved by 1, based on the p.i.p., as proposed by 4, 5. An application to the SS of a helicopter can be seen in 6 where a ‘central’ plant is proposed.…”

Feedback system design: the pole placement problem

“…Tracking and disturbance rejection [43], [45], [46] 2) Robust design algorithms [9], [45], [46] 3) Design with proper stable compensators [11], [45], [46] 4) Transfer function design [45], [46] 5) Simulataneous Design [9], [46] 6)…”