Perfluorinated 6-isopropyl-2,4,5-trimethylbenzonitrile

6 . 245 : Multivariable Control Systems

Let M be a complex matrix of rank one, i.e. M = pq′ where p, q are complex nby-1 matrices and ′ denotes Hermitean conjugation. Let μC(M) and μR(M) denote the structured singular values μ(M,∆) of M defined with ∆ = ∆C and ∆ = ∆R respectively, where ∆C is the cone of all diagonal matrices with complex entries, and ∆R is the cone of all diagonal matrices with real entries. (a) Express μC(M) and μR...

Science 6 . 245 : MULTIVARIABLE CONTROL SYSTEMS

So far, the optimization methods under consideration were presented for the continuous time case. This lecture describes a technique which allows one to apply the continuous time algorithms of H2 optimization, H-Infinity optimization, and Hankel optimal model reduction to discrete time systems. The technique is based on applying the familiar “Tustin” (or “bilinear”) CT to DT transformation. Whi...

2-Hy­droxy-6-isopropyl-3-methyl­benzoic acid

The title compound, C(11)H(14)O(3), is a multiple-substituted derivative of benzoic acid. Intra-cyclic C-C-C angles span a range of 117.16 (19)-122.32 (19)°. Apart from intra-molecular hydrogen bonds between hydroxyl and carboxyl groups, inter-molecular hydrogen bonds are present in the crystal structure, the latter ones giving rise to centrosymmetric carb-oxy-lic acid dimers.

2-Isopropyl-6-methyl­pyrimidin-4(3H)-one

The mol-ecular structure of the title compound, C(8)H(12)N(2)O, indicates that 2-isopropyl-6-methyl-pyrimidin-4-ol (the enol-form) undergoes an enol-to-keto tautomerism during the crystallization process. The pyrimidin-4(3H)-one group is essentially planar, with a maximum deviation of 0.081 (1) Å for the O atom. In the crystal structure, symmetry-related mol-ecules are linked into centrosymmeti...

6 . 245 : MULTIVARIABLE CONTROL SYSTEMS by A . Megretski Problem Set