Frequency-truncated system norms

Some applications require norm computation of frequency-truncated systems. A typical frequency-truncated system is one whose frequency response is rational in certain frequency bands and is zero in others. This note explains how to compute the L² norm of such systems.     

When does the H/sup /spl infin// fixed-lag smoothing performance saturate for a finite smoothing lag?

A notable difference between the H/sup 2/ and H/sup /spl infin// smoothing is that the achievable performance in the latter problem might "saturate" as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag. In this note, necessary and sufficient conditions under which such a saturation occurs are derived. In particular, it is shown that the H/sup /spl infin// performance saturates only if the H/sup /spl infin// norm of the optimal error system is achieved at the infinite frequency, i.e., if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable.     

Corrections to “On the structure of H∞control systems and related extensions”

The authors state that in the original paper (Kimura, Lu and Kawatani, ibid., vol. 36, p. 653-67, 1991) a lemma on (J,J')-losslessness is not correct. Its stated implications are also not fully correct. They give a counterexample to these claims and show how they can be fixed by strengthening the assumption     

Finding optimal ventilation control for highway tunnels

A control scheme for highway tunnels is designed based on a static model of the highway tunnel. The controller is designed to keep the exhaust levels inside the tunnel below given limits. The control is then simulated on a dynamical model of a highway tunnel.     

Control of systems with I/O delay via reduction to a one-block problem

In this paper, the standard (four-block) H/sup /spl infin// control problem for systems with a single delay in the feedback loop is studied. A simple procedure of the reduction of the problem to an equivalent one-block problem having particularly simple structure is proposed. The one-block problem is then solved by the J-spectral factorization approach, resulting in the so-called dead-time compensator (DTC) form of the controller. The advantages of the proposed procedure are its simplicity, intuitively clear derivation of the DTC form of the H/sup /spl infin// controller, and extensibility to the multiple delay case.     

Some properties of an upper bound for μ

A convex upper bound of the mixed structured singular value μ is analyzed. The upper bound is based on a multiplier method. It is simple, it can exploit low-rank properties, and it is shown to be less conservative than the well-known (D,G)-scaling. A direct relationship with (D,G)-scaling is given. The upper bound can be modified to one that is continuous with an explicit Lipschitz constant     

Rank-one LMIs and Lyapunov's inequality

We describe a new proof of the well-known Lyapunov's matrix inequality about the location of the eigenvalues of a matrix in some region of the complex plane. The proof makes use of standard facts from quadratic and semidefinite programming. Links are established between the Lyapunov matrix, rank-one linear matrix inequalities (LMI), and the Lagrange multiplier arising in duality theory     

On H/sub 2/ control of systems with multiple I/O delays

The H/sub 2/ optimal control problem of systems with multiple I/O delays is solved. The problem is tackled by first transforming it to what is called the two-sided regulator problem. The latter is solved using orthogonal projection arguments and spectral factorization. The resulting controller is an interconnection of rational blocks, nonrational blocks having finite impulse response, and delay operators, all of which are implementable.     

Heterozygosity for a point mutation in an invariant splice donor site of dihydropyrimidine dehydrogenase and severe 5-fluorouracil related toxicity

Dihydropyrimidine dehydrogenase (DPD) is responsible for the breakdown of the widely used antineoplastic agent 5-fluorouracil (5-FU), thereby limiting the efficacy of the therapy. It has been suggested that patients suffering from 5-FU toxicities due to a low activity of DPD are genotypically heterozygous for a mutant allele of the gene encoding DPD. In this study we investigated the cDNA and a genomic region of the DPD gene of a cancer patient experiencing severe toxicity following 5-FU treatment for the presence of mutations. Although normal activity of DPD was observed in fibroblasts, the DPD activity in leucocytes of the cancer patient proved to be in the heterozygous range. Analysis of the DPD cDNA showed heterozygosity for a 165bp deletion that results from exon skipping. Sequence analysis of the genomic region encompassing the skipped exon showed that the tumour patient was heterozygous for a G-->A point mutation in the invariant GT splice donor sequence in the intron downstream of the skipped exon. So far, the G-->A point mutation has also been found in 8 out of 11 patients suffering from a complete deficiency of DPD. Considering the frequent use of 5-FU in the treatment of cancer patients, the severe 5-FU-related toxicities in patients with a low activity of DPD and the high frequency of the G-->A mutation in DPD deficient patients, analysis of the DPD activity and screening for the G-->A mutation should be routinely carried out prior to the start of the treatment with 5-FU.     

Polynomial solutions to H∞ problems

The paper presents a polynomial solution to the standard H_∞-optimal control problem. Based on two polynomial J-spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomial J-spectral factorization problems.