Robustness of multivariable feedback systems: analysis and optimal desing

The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H∞-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution

Robustness of multivariable feedback systems

The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H∞-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution.</p

Robustness of multivariable feedback systems

The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H∞-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution.</p

Analysis of clinically relevant variants from ancestrally diverse Asian genomes

Asian populations are under-represented in human genomics research. Here, we characterize clinically significant genetic variation in 9051 genomes representing East Asian, South Asian, and severely under-represented Austronesian-speaking Southeast Asian ancestries. We observe disparate genetic risk burden attributable to ancestry-specific recurrent variants and identify individuals with variants specific to ancestries discordant to their self-reported ethnicity, mostly due to cryptic admixture. About 27% of severe recessive disorder genes with appreciable carrier frequencies in Asians are missed by carrier screening panels, and we estimate 0.5% Asian couples at-risk of having an affected child. Prevalence of medically-actionable variant carriers is 3.4% and a further 1.6% harbour variants with potential for pathogenic classification upon additional clinical/experimental evidence. We profile 23 pharmacogenes with high-confidence gene-drug associations and find 22.4% of Asians at-risk of Centers for Disease Control and Prevention Tier 1 genetic conditions concurrently harbour pharmacogenetic variants with actionable phenotypes, highlighting the benefits of pre-emptive pharmacogenomics. Our findings illuminate the diversity in genetic disease epidemiology and opportunities for precision medicine for a large, diverse Asian population.</p