Impulsive modes and causality in singular systems

Embedding singular linear system with initial condition into distribution space

“…(2) Anf satisfying the requirement in Definition 2.3 will be called an extension of f for short in following. (3). For given extensionf , solution of (2.12), if exists, is unique.…”

“…Such impulse phenomenon distinguishes the singular linear system from the standard one [3][4][5][6][7][8].…”

Solutions of generalized linear matrix differential equations which satisfy boundary conditions at two points

“…Linear systems of type (1) are closely related to matrix pencil theory, since the algebraic geometric, and dynamic properties stem from the structure by the associated pencil sF − G. Given F, G ∈ M nm and an indeterminate s ∈ F, the matrix pencil sF − G is called regular when m = n and det(sF − G) = 0, see [10,28,38,43,47]. In any other case, the pencil will be called singular.…”

“…The class of sF −G is characterized by a uniquely defined element, known as a complex Weierstrass canonical form, sF w − G w , see [10,28,38,43,47], specified by the complete set of invariants of the pencil sF − G. This is the set of elementary divisors (e.d.) obtained by factorizing the invariant polynomials f i (s,ŝ) into powers of homogeneous polynomials irreducible over field F .…”

A Deterministic Approach for Optimal Recursive Prediction of Singular Discrete-Time Systems

“…For discrete-time descriptor systems, the state estimation is presented recursively and the resulting generalized Kalman filter has been intensively studied (see e.g. (Dai, 1989), (Darouach et al, 1993), (Deng and Liu, 1999), (Ishihara et al, July 2004a), (Keller et al, 1992), (Nikoukhah et al, 1999), (Nikoukhah et al, 1992), (Zhang et al, 1999), (Zhang et al, 1996)). Different formulations have been proposed in order to deal with this problem.…”