2 citations · 2 across the 6 of their papers we have counts for
8 papers
The Indefinite Summation Problem for the Laurent Ring
Shiva Shankar
This article solves the Indefinite Summation Problem (ISP) for the difference ring , where is the Laurent ring of shift operators on the lattice , and is any…
The coarsest lattice that determines a discrete multidimensional system
Debasattam Pal, Shiva Shankar
A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice . This paper shows that it is determined…
The Canonical Controller for Distributed Systems
Shiva Shankar
This paper generalises results of Willems-Trentelman, and van der Schaft, on achievable behaviours, to the case of linear distributed systems defined by partial differential or dif…
Controllability and Vector Potential
Shiva Shankar
Kalman's fundamental notion of a controllable state space system \cite{k} has been generalised to higher order systems by Willems \cite{w}, and further to distributed systems defin…
Structurally Stable Properties of Control Systems
Shiva Shankar
Talk dedicated to the 110th anniversary of L.S.Pontryagin. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow.
The Generic Degree of Autonomy
Shiva Shankar, Paula Rocha
This paper calculates the degree of autonomy of a generic autonomous n-D system given by the kernel of a partial difference operator. The calculation implies that attaching a gener…
The Hautus Test and Genericity Results for Controllable and Uncontrollable Behaviors
Shiva Shankar
This paper generalizes the classical Hautus Test to systems described by partial differential equations.
Periodic behaviors
Diego Napp, Marius van der Put, Shiva Shankar
This paper studies behaviors that are defined on a torus, or equivalently, behaviors defined in spaces of periodic functions, and establishes their basic properties analogous to cl…