Forward, backward, and symmetric solutions of discrete ARMA representations

Abstract

Δημοσιεύσεις μελών--ΣΤΕΦ--Τμήμα Μηχανικών Πληροφορικής, 2001The main objective of this paper is to determine a closed formula for the forward, backward, and symmetric solution of a general discrete-time Autoregressive Moving Average representation. The importance of this formula is that it is easily implemented in a computer algorithm and gives rise to the solution of analysis, synthesis, and design problems

Alternate checking criteria for reachable controllability of rectangular descriptor systems

“…A square system [E A B] ∈ Σ n,n,r is called regular if there exists λ ∈ C such that the matrix pencil (λE − A) is invertible, where C denotes the set of complex numbers. A square system [E A B] ∈ Σ n,n,r is called state space if the matrix E = I n , the identity matrix of size n. Descriptor systems arise naturally in various real world applications [5,6,10,22,23,24,31] as these are general enough to describe the intrinsic properties of underlying physical systems. However, the analysis of descriptor systems is more delicate than state space systems in the sense that the solutions may have impulses if the input is not sufficiently smooth or the initial condition is not suitably chosen.…”

Modeling, reachability and observability of linear multivariable discrete time systems

“…We denote by µ the sum of the degrees of the infinite elementary divisors of A(s) i.e. 56) and is equal to the sum of the orders of its poles at infinity.…”

“…Now, setting k = 0 in (2.7) we obtain Definition 2.6. [56] The set of consistent initial values of (2.1) is defined as…”

“…A notable distinction from state space systems and continuous time descriptor systems, is that discrete time descriptor systems do not have a solution for every set of initial values, as was commented in [19] and later in [55,56]. That is, in order for the descriptor system (2.1) to have a solution, the initial values need to satisfy certain consistency constraints.…”

“…the system (4.1) can be rewritten as Various methods of approach have been established to compute their solution and study properties like controllability and observability. A straightforward approach has been used in [30,37,52,116,118] for the continuous time case and in [4,40,53,56,58,89] for the discrete time case, through the use of the Jordan Pairs and the Laurent expansion at infinity of the polynomial matrix A(σ). A different method for continuous time has also been used in [107].…”