Structural properties of positive linear time-invariant difference-algebraic equations

Asymptotic Properties for Half-linear Difference Equations

Dedicated to Prof. Jaroslav Kurzweil on the occasion of his 80th birthday Abstract. Asymptotic properties of the half-linear difference equation (∗) ∆(an|∆xn| α sgn∆xn) = bn|xn+1| α sgnxn+1 are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to (∗) are considered too. Our approach is based on a classification of solutions of (...

Structural Controllability of Linear Time-invariant Systems

One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair (A,B) whose nonzero entries are distinct parameters, is structurally controllable if values can be assigned to the parameters which cause the resulting matrix pair to be controllable. In this paper...

Some properties of algebraic difference equations of first order

Algebraic Difference Equations

Sharp algebraic periodicity conditions for linear higher order difference equations

In this paper we give easily verifiable, but sharp (in most cases necessary and sufficient) algebraic conditions for the solutions of systems of higher order linear difference equations to be periodic. The main tool in our investigation is a transformation, recently introduced by the authors, which formulates a given higher order recursion as a first order difference equation in the phase space...