Condition and algorithm for simultaneous stabilization of linear plants

This paper is devoted to the problem of simultaneous stabilization of linear plants. It is shown that four given plants pi(s), i = 1,2.3,4 are simultaneously stabilizable if and only if there exist four stable polynomials H-i(s). i = 1,2,3,4 which simultaneously satisfy two polynomial equations. If we can only find four stable H-i(s), i = 1.2,3,4 to satisfy one of the two polynomial equations. then two controllers c(1)(s) and c(2)(s). having a common denominator or numerator. can be obtained such that c(1)(s) simultaneously stabilizes p(1)(s) and p(3)(s), and c(2)(s) simultaneously stabilizes p(2)(s) and p(4)(s), which is called the simultaneous stabilization in groups. Based on such two controllers. a design algorithm for the simultaneous stabilization of three plants is induced. (C) 2001 Elsevier Science Ltd. All rights reserved.