Amol Sasane

Compactness and nuclearity of the Hankel operator and internal stability of infinite-dimensional state linear systems

We examine the relationships between the exponential (or strong) stability of certain classes of regular linear systems and the compactness and nuclearity properties of the Hankel operator. New sufficient conditions for nuclearity are given for exponentially stable regular linear systems with an analytic semigroup.

Time-autonomy versus time-controllability

We study systems whose dynamics are described by systems of linear constant coefficient partial differential equations in a behavioural framework. Questions about the notion of autonomy and controllability are addressed with special importance given to the time-evolution. We investigate consequences of time-autonomy for time-controllability.

Hankel norm approximation for well-posed linear systems

The sub-optimal Hankel norm approximation problem is solved for a well-posed linear system with generating operators (A,B,C) and transfer function G satisfying some mild assumptions. In the special case of the sub-optimal Nehari problem, an explicit parameterization of all solutions is obtained in terms of the system parameters A, B, C and G(0).

Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems

The optimal Hankel norm approximation problem is solved under the assumptions that the system Σ(A, B, C) is an exponentially stable, regular Pritchard-Salamon infinite-dimensional system. An explicit parameterization of all solutions is obtained in terms of the system parametersA, B, C.

Time-Autonomy and Time-Controllability of 2-D Behaviours that are Tempered in the Spatial Direction

AbstractThis paper studies the notions of time-autonomy and (exact) time-controllability of behaviours with respect to a certain mild space, which while being not too general, encompasses natural partial differential equation solutions and excludes certain pathological ones. We give an algebraic characterization of the property of time-autonomy and also give necessary and sufficient conditions for the time-controllability of behaviours with respect to the space of distributions on

On Riccati Equations in Banach Algebras

\mathbb{R}^2

Inertia theorems for operator Lyapunov inequalities

that are tempered in the spatial direction.

State-Space Formulas for the Nehari-Takagi Problem for Nonexponentially Stable Infinite-Dimensional Systems

This paper develops a behavioural framework to study controllability of systems whose dynamics are described by systems of linear, constant coefficient partial differential equations. Questions about the notion of controllability are addressed with special importance given to the time-evolution. Algebraic conditions concerning time-controllability are proved.