Yossi Peretz

Jerusalem College of Technology | JCT · Computer Sciences

In this paper, we propose a new digital Hard-Successive-Interference-Cancellation (HSIC), the Alternating Projections-HSIC (AP-HSIC), an innovative fast computational feedback algorithm that deals with various destructive phenomena from different types of interferences. The correctness and convergence of the proposed algorithm are provided, and its...

Various destructive weather and physical phenomena affect many parameters in the radio layer (i.e., affecting the wireless paths Over-The-Air (OTA)) of many outdoor-to-outdoor wireless systems. These destructive effects create polarization torsion and rotation of the signals propagating in space and cause the scattering of wireless spatial paths. T...

In this article, we consider the problem of the existence of rational {1, 2}-pseudo-inverses for rational multivariable matrix-valued functions. We prove that any rational multivariable the matrix-valued function has rational {1, 2}-pseudo-inverse and we describe the set of all {1, 2}-pseudo-inverses of a given function, in terms of rational free p...

A new parallel algorithm for the max-flow problem on directed networks with single-source and single-sink is proposed. The algorithm is based on tree sub-networks and on efficient parallel algorithm to compute max-flows on the tree sub-networks. The latter algorithm is proved to be work-optimal and time-optimal. The parallel implementation of the c...

An algorithm is proposed for the solution of the NP-hard problem of simultaneous nonsymmetric algebraic Riccati equations over finite fields. The proposed algorithm has an application to the solution of some structured quadratic polynomial equations over finite fields with complexity of O˜2(nℓmax+n+ℓmax) for m⋅n variables and m⋅n equations over F2,...

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the...

The widespread deployment of 5G wireless networks has brought about a radical change in the nature of mobile data consumption. It requires the deployment of Long Term Evolution to the unlicensed spectrum (LTE-U) to alleviate the shortage of available licensed spectrum while Wi-Fi is the most dominant radio access technology in the unlicensed spectr...

To cope with the shortage of available licensed spectrum, 4th Generation Long Term Evolution (4G LTE) is expected to be deployed also in the unlicensed spectrum. This raises the problem of the coexistence of multiple operators. Obviously, a Software Defined Networking (SDN) based control approach can utilize the radio bandwidth by coordinating betw...

For a given system with time-invariant affine uncertainties, ranging in a unit hypercube or, equivalently, in a hyper-rectangle, new LMI sufficient conditions for the verification of a given simultaneous static-output-feedback for hypercube nodes, being robust static-output-feedback for the whole system, are proved. The conditions generalise previo...

A randomised algorithm is proposed for computing globally optimal static-output-feedbacks for large-scale systems. The algorithm is based on the Ray-Shooting Method and involves some heuristics to accelerate the search. We also improve the basic Ray-Shooting Algorithm and make the search in the controller parameter-space (which generally, is much m...

Randomized and deterministic algorithms for the problem of LQR optimal control via static-output-feedback (SOF) for discrete-time systems are suggested in this chapter. The randomized algorithm is based on a recently introduced randomized optimization method named the Ray-Shooting Method that efficiently solves the global minimization problem of co...

A randomized Branch-And-Bound algorithm is suggested for the problem of Robust Stabilization Via Static-Output-Feedback (RSOF). Given a system with affine uncertainties, where the uncertainty parameters vary in the unit hyper-cube, and given a Static-Output-Feedback (SOF) for the system defined by the middle point of the hyper-cube, we define a ne...

A new theorem regarding the robust stability hypercube-tolerance with respect to the specific system defined by the middle-point of a hypercube and a given stabilizing static-output-feedback for it, is proved. Based on the theorem and using the Ray-Shooting Method, a randomized algorithm for the problem of robust stabilization via static-output-fee...

TP-I (Tsafenat-Paaneah-I) and TP-II (Tsafenat-Paaneah-II) are two public-key encryption schemes based on simultaneous algebraic Riccati equations over finite fields, which were proposed by Peretz in 2016 [9]. In this research, we discovered the hidden linear structure of TP-I and TP-II, respectively. Hence, we are going to show how can one break th...

A randomized algorithm is suggested for the syntheses of optimal PID controllers for MIMO coupled systems, where the optimality is with respect to the H ∞-norm, the H 2-norm and the LQR functional, with possible system-performance specifications defined by regional pole-placement. Other notions of optimality (e.g., mixed H 2 /H ∞ design, controller...

In this article we suggest a randomized algorithm for the LQR (Linear Quadratic Regulator) optimal-control problem via static-output-feedback. The suggested algorithm is based on the recently introduced randomized optimization method called the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over...

Recently a new prametrization of all the exact pole-assignment state-feedbacks for LTI systems was introduced. The parametrization is based on the assumption that the given set of eigenvalues to be assigned to the closed loop, contains sufficient number of pure-real numbers. The parametrization shows a multivariable polynomial dependent of the set...

A new digital signature based on algebraic Riccati equation is suggested. The signature outperforms any known undefeated signatures in terms of time for signing and verification, for security levels of 2^128 and 2^256. There is no free luch and indeed the price is in memmory, but still lower than any scheme based on multivariable quadratic equation...

In this article we provide a parametrization of all the exact pole-assignment state-feedbacks for LTI systems, when the set of poles to be assigned contains sufficient number of real eigenvalues. We also refute a recent conjecture concerning the explicit form of all the state-feedbacks assigning a given set of poles to the closed-loop.

A randomised optimisation method, called the ray-shooting method that efficiently solves the minimisation problem of continuous functions over compact non-convex unconnected regions, was introduced recently. Based on the ray-shooting method, an algorithm is suggested for solving the problems of structured and structured-sparse stabilising static-ou...

The presentation contains the talk I gave in the ACA 2016 conference, Kassel, Germany,1-4 August 2016. In the talk I have explained how can one define a asymmetric public-key cryptographic system using a set of algebraic Riccati equations over a finite field. The security of the system represented is based on the problem of Nonsymmetric Simoultaneo...

A new randomized algorithm is suggested, for extracting static-output-stabilizing-feedbacks, with approximately minimal-norm, for LTI systems. The algorithm has two similar stages, where in the first one the feasibility problem is solved, and in the second one the optimization problem is solved. The formulation is unified for the feasibility and fo...

New multivariable asymmetric public-key encryption schemes based on the NP-complete problem of simultaneous algebraic Riccati equations over finite fields are suggested. We also provide a systematic way to describe any set of quadratic equations over any field, as a set of algebraic Riccati equations. This has the benefit of systematic algebraic cr...

In this article, we give sufficient conditions for the existence of contractive solutions for the Non-Symmetric Algebraic Riccati Equation.The conditions are given in terms of the matrix of the coefficients–only. We also provide sufficient conditions for unique contractive solution (which is a unique minimal-norm solution). The results are generali...

In this article, we give a complete characterization (geared towards a parametrization) of all the static feedbacks of a given LTI system triplet, in terms of the coefficients of some reduced order Riccati equation, with simultaneously stabilizing solutions and structural constraints – on the coefficients.

It is well known that linear system theory, Lax-Phillips scat-tering theory, and operator model theory for a contraction operator are all intimately related. A common thread in all three theories is a contractive, analytic, operator-valued function on the unit disk W (z) having a represen-tation of the form W (z) = D + zC(I − zA) −1 B, known, depen...

It is well known that linear system theory, Lax-Phillips scattering theory, and operator model theory for a contraction operator are all intimately related. A common thread in all three theories is a contractive, analytic, operator-valued function on the unit disk W(z) having a representation of the form W(z) = D + zC(I - zA)B-1, known, depending o...

In this paper we introduce and develop analogs of de Branges-Rovnyak spaces in the setting of lower triangular integral operators and the corresponding coisometric realization theorem.

In this paper we prove generalized Herglotz representation theorems for bounded upper triangular operators with nonnegative real part when the base “point” (in fact a diagonal operator) is different from 0.

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the “nonstationary setting”, i.e. when one consider...

In this paper we study analogs of de Branges-Rovnyak spaces and prove a realization theorem in the setting of upper triangular matrices.

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometrie and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the "nonstationary setting", i.e. when one consider...

For upper triangular operators with nonnegative real part, we derive generalized Herglotz representation theorems in which the main operator is coisometric, isometric, or unitary. The proofs are based on the representation theorems for upper triangular contractions considered earlier by D. Alpay and Y. Peretz.

The Hilbert space of lower triangular Hilbert–Schmidt operators on the real line is a natural analogue of the Hardy space of a half-plane, where the complex numbers are now replaced by matrix-valued functions. One can associate with a bounded operator its “values” at a matrix-valued function [see Ballet al.,Oper. Theory Adv. Appl.56(1992), 52–89],...

Spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations of Schur functions. In this paper we show that similar realizations exist in the “nonstationary setting”, i.e. when one considers upper triangular contractions (which appear in time-variant system theory as “transfer functions” of dissipative s...

The aim of this paper is to solve a matrix-valued version of the Nevanlinna-Pick interpolation problem for H2 functions. We reduce this problem to a Nevanlinna-Pick interpolation problem for Schur functions and obtain a linear fractional transformation which describes the set of all solutions.