A reformulation of augmented basic interpolation problem and an application to H∞ control

Abstract

MSC:In this paper we present a new formulation of the augmented basic interpolation problem (aBIP) with rational matrices, in terms of the stability of four rational matrices, so that the aBIP transforms into a purely linear-algebraic problem. Actually, the existing interpolation condition, given by an integral, is replaced by stability of a rational matrix. The new condition is applied to the H ∞ optimal control of one-block plants having imaginary axis invariant zeros. A new parameter in the parametrization of H ∞ optimal controllers is revealed, which is given in terms of the derivative of the closed-loop system at the imaginary axis invariant zeros of the plant. The H ∞ optimal control algorithm is illustrated by an example, and compared to the existing algorithms.

New interpolation solution and application in system modeling and optimal control with prescribed distance to instability

“…Proof Proposition 2 is actually Theorem 1 in [25]. Note that in Theorem 1 in [25], A is an arbitrary matrix (not satisfying Assumption 1).…”

“…Proof Proposition 2 is actually Theorem 1 in [25]. Note that in Theorem 1 in [25], A is an arbitrary matrix (not satisfying Assumption 1). By Proposition 2, we see that, taking D 1, the interpolation conditions (2.2), (2.3), (2.4), and k 1 U k 1 6 1 coincide with the interpolation conditions of the problem aBIP.…”

“…In the following proposition, we consider proper solutions U to Problem .Proposition Given arbitrary γ > 0, and matrices A , and R satisfying , a proper stable RM U satisfies the conditions , , and if and only if it is proper and stable and satisfies the conditions , , and where the notation means .Proof Proposition is actually Theorem 1 in . Note that in Theorem 1 in , A is an arbitrary matrix (not satisfying Assumption ). □…”