Robust Stabilization of a Family of Plants with Varying Number of Right Half Plane Poles

Robust stability condition for a class of time-delay plants with uncertainty

“…On the other hand, the influence of ∆(s) toward to input-output property is a tendency to decrease if the sensitivity function S(s) denoted by (4) becomes smaller. The sensitivity function S(s) is equivalent to the transfer function from the disturbance d to the output y.…”

“…Several papers have been considered on robust stabilization problem [1][2][3][4][5][6]. Doyle and Stein built the basis for this problem [1], and the condition for plants with the multiplicative uncertainty and the additive uncertainty was shown.…”

Maximally robust controllers for multivariable systems

“…The work presented in this paper is related to the problem of maximizing the robust stability radius for systems subject to unstructured additive perturbations [25], [6], [23], [24]. In [6] it was shown that this problem is equivalent to a Nehari approximation.…”

“…Our approach is as follows: From the work in [25], [24], and [6] the maximum robust stability radius r 1 is the inverse of the smallest achievable H ∞ norm among all interpolating functions T = {K(I − GK) −1 }, as K varies over the set of all internally stabilizing compensators of G. Using an allpass dilation technique, the set of all optimal interpolating functions T 1 = {T ∈ T : T ∞ = r …”

“…Theorem 3.1 (see [25], [6], [24]). Let G ∈ RL ∞ and suppose that (G, K) ∈ S. Then (G, K) is (r, w) robustly stable if and only if wK(I − GK) −1 ∞ ≤ r −1 .…”