相关论文: On real and observable rational realizations of in…

Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…

We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees…

Rational observers are to be constructed for rational systems while polynomial observers are to be constructed for polynomial systems. An observer synthesis procedure is formulated. First an output-based rational realization is synthesized…

In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the…

We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…

Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…

We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…

In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…

This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…

A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…

This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…

The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of…

We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…

The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…

We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…

Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.

In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…