arXiv subjects

Amol J. Sasane

Publications and source records attributed to Amol J. Sasane.

3 recordsLinked to original sources

arXiv2010

Extension of the $ν$-metric: the $H^\infty$ case

An abtract $ν$-metric was introduced by Ball and Sasane, with a view towards extending the classical $ν$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. In this short note, we give an additional concrete special instance of the abstract $ν$-metric, by verifying all the assumptions demanded in the abstract set-up. This example links the abstract $ν$-metric with the one proposed by Vinnicombe as a candidate for the $ν$-metric for nonrational plants.

math.OC↗

arXiv2010

On Riccati equations in Banach algebras

Let $R$ be a commutative complex Banach algebra with the involution $\cdot ^\star$ and suppose that $A\in R^{n\times n}$, $B\in R^{n\times m}$, $C\in R^{p\times n}$. The question of when the Riccati equation $$ PBB^\star P-PA-A^\star P-C^\star C=0 $$ has a solution $P\in R^{n\times n}$ is investigated. A counterexample to a previous result in the literature on this subject is given, followed by sufficient conditions on the data guaranteeing the existence of such a $P$. Finally, applications to spatially distributed systems are discussed.

math.OC↗

arXiv2010

Extension of the $ν$-metric

We extend the $ν$-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.

math.OC↗