Avraham Feintuch

Paper: Uniformly optimal control of linear feedback systems

The problem of uniformly optimal control is posed in the context of linear time-varying discrete-time systems; the controller is optimal uniformly over a pre-specified set of exogenous signals. Existence of an optimal controller is proved and a formula for the minimum cost is derived. The time-invariant case is treated in the frequency domain. It is shown that for time-invariant systems an optimal time-varying controller is no better than an optimal time-invariant controller.

Uniformly optimal control of linear time-varying systems

Abstract An optimal control problem is formulated in the context of linear, discrete-time, time-varying systems. The cost is the supremum, over all exogenous inputs in a weighted ball, of the sum of the weighted energies of the plants input and output. The controller is required to be causal and to achieve internal stability. Existence of an optical controller is proved and a formula for the minimum cost is derived.

On the sensitivity minimization problem for linear time varying periodic systems

An optimal control problem is formulated in the context of linear, discrete-time, periodic systems. The cost is the supremum over all exogenous inputs in a weighted ball of plant inputs. The controller is required to be causal, periodic of the fixed order of the system and to achieve internal stability. Existence of an optimal controller is proved and a formula for the minimum cost is derived.

On Asymptotic Toeplitz and Hankel Operators

An operator T is asymptotic Toeplitz if for S the unilateral shift, the sequence {S ✹n n TS n } converges. It is asymptotic Hankel if for J n the permutation insometry on the subspace determined by the first n coordinate vectors, the sequence {J n TS n+1 } converges. The relationship between these notions is studied and operator analogues of the A.A.K. distance formulae in terms of the s numbers of a Hankel operator are obtained.

Brief paper: Infinite chains of kinematic points

In formulating the stability problem for an infinite chain of cars, state space is traditionally taken to be the Hilbert space @?^2, wherein the displacements of cars from their equilibria, or the velocities from their equilibria, are taken to be square summable. But this obliges the displacements or velocity perturbations of cars that are far down the chain to be vanishingly small and leads to anomalous behaviour. In this paper an alternative formulation is proposed wherein state space is the Banach space @?^~, allowing the displacements or velocity perturbations of cars from their equilibria to be merely bounded.

On strong stabilization for linear time-varying systems

Abstract This paper deals with the strong stabilization problem for linear time-varying systems and gives a sufficient condition, in terms of the coprime factors, for the existence of strong stabilizers for such a system.

On the strong stabilization of slowly time-varying linear systems

Abstract This paper considers the strong stabilization problem: Given a linear time-varying system which is stabilizable by dynamic feedback, when can the stabilizer be chosen to be itself stable? We consider here the case of the algebra of discrete-time time-varying systems which are slowly time varying.

On Pole Assignment for a Class of Infinite Dimensional Linear Systems

Let

Gain optimization for distributed plants

\{ {A,B} \}

Strong Causality Conditions and Causal Invertibility

be an infinite dimensional linear system where A is normal with compact resolvent and the input space is finite dimensional. Then the controllability of