An iterative technique to adjust ripple in a bandpass filter has been developed by curve‐fitting numerical data. It gives an approximate relation of ripple against filter coupling coefficients and resonator resonant frequencies instead of finding a Jacobian matrix for each individual filter, in exchange for making more iterations. Numerical examples show reasonable convergence for Chebyshev filters up to the 16th‐order, coupled quadruplets, coupled triplets and folded cross‐coupled filters. A bandpass filter for a radio telescope in Yebes, Spain is designed and measured, a tenth‐order superconducting spiral filter with 7% bandwidth, 2295 MHz centre frequency, <0.1 dB ripple and overall substrate size 30 mm × 8 mm. The 11 iterative simulations totalled 8.5 h of computer processing time.

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This paper concerns the robust stabilization of continuous-time polytopic systems subject to unknown but bounded perturbations. To tackle this problem, the attractive ellipsoid method (AEM) is employed. The AEM aims to determine an asymptotically attractive (invariant) ellipsoid such that the state trajectories of the system converge to a small neighborhood of the origin despite the presence of nonvanishing perturbations. An alternative form of the elimination lemma is used to derive new LMI conditions, where the statespace matrices are decoupled from the stabilizing Lyapunov matrix. Then a robust state-feedback control law is obtained by semi-definite convex optimization, which is numerically tractable. Further, the gain-scheduled state-feedback control problem is considered within the AEM framework. Numerical examples are given to illustrate the proposed AEM and its improvements over previous works. Precisely, it is demonstrated that the minimal size ellipsoids obtained by the proposed AEM are smaller compared to previous works, and thus the proposed control design is less conservative.

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