Leonard Weiss

On the controllability of delay-differential systems.

Controllability type applicable to optimal control problems for systems described by delay differential equations

Controllability, Realization, and Stability of Discrete-Time Systems.

The following problems are discussed and solved in this paper: finding computable necessary and sufficient conditions for complete reachability and complete observability of a linear, time-varying, discrete-time system; finding sufficient conditions for local controllability of nonlinear discrete-time systems; relating reachability to the concept of discrete Pfaffian systems; obtaining a minimal-dimension difference equation (with possibly variable coefficients) from a given input/output function of a system; finding necessary and sufficient conditions for Lyapunov stability and finite-time stability of nonlinear difference equations; and, giving an algorithm for determining whether a linear difference equation is stable in the finite-time sense.

Atoms for Peace

Did the 50-year-old Atoms for Peace program accelerate nuclweapons proliferation? The juhas been in for some time on this question, and the answer is yes.

Contributions to linear system theory

Abstract The paper begins with an axiomatic definition of a dynamical system and then considers in detail the class of systems governed by a set of first order linear differential equations in the state variables. New results are presented in the theory of controllability, observability and canonical structure of such systems. A fairly complete discussion is given of the relationship between internal system structure (as represented by the state-variable differential equation) and external system structure (as represented by the systems ‘weighting pattern’ or impulse response, and input-output differential equation). Fundamental roles in the discussion are played by the concepts of ‘anticausal’ controllability, i.e. controllability of the system under the action of time-reversal, and ‘differential’ controllability, i.e. controllability over arbitrarily small intervals. Similarly for ‘anticausal’ and ‘differential’ observability.

An algebraic criterion for controllability of linear systems with time delay

A new algebraic sufficient condition for controllability of linear time-varying delay-differential systems is established, which reduces to the conventional one for ordinary differential systems when the delay term is absent.

Doležal's theorem, linear algebra with continuously parametrized elements, and time-varying systems

Many problems in the theory of time-invariant systems involve the characterization and representation of the range or null space of a given matrix as the major ingredient in their solution. The solution of similar problems for time-varying systems is generally difficult because of the lack of a simple representation of the aforementioned spaces. Dole~als theorem [1] essentially yields a condition under which simple representations of the range and null spaces of continuously parametrized matrices are extant. The theorem therefore provides a recipe for generalizing a wide class of results for time-invariant systems to the time-varying case. In a more general context, it enables a natural extension of some aspects of linear algebra to the situation where elements are continuously parametrized. The original proof of the theorem contains a lemma whose proof in [1] is slightly faulty. In this paper approach the theorem from a somewhat different initial direction and provide an alternate proof which dovetails with that given in [1]. Various algebraic results stemming from the main theorem are presented and an outline of some important applications of these results to the theory of time-varying systems is given.

Finite time stability with respect to time-varying sets

Abstract Sufficient conditions are developed for solutions to certain classes of nonlinear continuous-time systems to be located within certain a priori specified sets over a given time interval. Analogous results are obtained for discrete-time systems, and in both cases such conditions are shown to be necessary under mild additional hypotheses.

U.S.-INDIA NUCLEAR COOPERATION Better Later than Sooner

On July 5, 2005, President George W. Bush and Indian Prime Minister Manmohan Singh signed an agreement pledging their governments to actions designed to culminate in a formal nuclear cooperation agreement that would end a three-decade U.S. nuclear embargo against India. Although the formal agreement has not yet received final approval from Congress, concerns about the consequences of the agreement, particularly its possible adverse effect on the Treaty on the Non-Proliferation of Nuclear Weapons (NPT) and the worldwide nonproliferation regime, have made the agreement controversial. This article traces the events that led to the Bush-Singh meeting, explicates the current situation, examines the arguments for and against the proposed agreement, and makes some preliminary judgments regarding the agreements effects on the nonproliferation regime. The failure to prevent Indias 1998 nuclear tests with the threat of sanctions (because the Indians calculated that long-term U.S. resolve was not sustainable) set in motion a chain of events that would ultimately end the nuclear embargo. However, the conditions for a better U.S.-India nuclear agreement—from a nonproliferation perspective—will inevitably arise if the current proposed agreement is not adopted.

Stability of non-linear discrete-time systems†

Converse theorems for Liapunov stability of non-linear difference equations are presented, which improve upon past results in this area. The main improvement consists in not assuming that solutions can be extended backward in time. When such assumptions are made, however, it is shown that necessary conditions for finite-time stability of non-linear difference equations can be readily derived.

India and the NPT

Abstract Indias nuclear development has been accompanied by a dual track strategy of developing and building weapons while criticising the non-proliferation regime as discriminatory and simultaneously making public statements and proposals in favour of nuclear disarmament. But with international progress likely on aspects of nuclear disarmament over the next few months, India will be in the spotlight at the forthcoming 2010 Non-Proliferation Treaty (NPT) Review Conference to help move the disarmament and non-proliferation agenda forward. This article proposes that India meet this challenge by announcing specific commitments on permanently ending nuclear testing and plutonium production for weapons by a set date. In the course of reaching this conclusion, the article traces the history of Indias role in the development of the international non-proliferation regime, its proposals on disarmament, and also its relationship with the United States with respect to Indias nuclear development and ambitions.