The differential rational representation algebra on a linear differential algebraic group

Differential Equations and Linear Algebra

where D = d/dt is the basic differentiation operator on functions. (The j-th derivative operator, for j ≥ 1, is Dj , and we consider the identity operator I as D0, since it is standard to regard the zero-th derivative of a function as the function itself: D0(y) = y for all functions y.) We call (1.2) an n-th order linear differential operator since the highest derivative appearing in it is the ...

Algebraic Differential Equations and Rational Control Systems

SYSTEMS Yuan Wang Mathematics Department, Florida Atlantic University, Boca Raton, Fl 33431 (407)367-3317, E-mail: y [email protected] Eduardo D. Sontag Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 (908)932-3072, E-mail: [email protected] ABSTRACT An equivalence is shown between realizability of input/output operators by rational control systems and high orde...

Bounds and algebraic algorithms in differential algebra: the ordinary case

Consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal. We propose a bound on the orders of derivatives occurring in all intermediate and final systems computed by this algorithm. We also reduce the problem of conversion of a regular decomposition of a radical differential ideal from one ranking to another to a purely algebraic problem.

Linear Differential Behaviors Described by Rational Symbols

The behavior of a linear time-invariant differential system is defined as the set of solutions of a system of linear constantcoefficient differential equations. However, these behaviors can be represented in many other ways, for example, as the set of solutions of a system of equations involving a differential operator in a matrix of rational functions, rather than in a matrix of polynomials. T...

Differential Equations and Linear Algebra Notes