Using the modern time-series analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimator, non-regular descriptor discrete-time stochastic linear systems are researched. Under assumption 1~3, an asymptotically stable reduced-order Wiener state estimator for descriptor systems is given by using projection and block matrix theori...

This report treats some basics on parameter identification in linear time invariant descriptor systems, both time continuous and time discrete. It is shown how identification methods for normal state space systems can be used by transforming the descriptor system to state space form. It is also examined how identification can be performed in the frequency domain.

The positive stabilization problem of discrete-time descriptor systems by means of state-feedback control is studied here. Thus, conditions are developed for a state-feedback controller to make the controlled descriptor system simultaneously stable and positive. An illustrative example is provided to illustrate the proposed approach.

We present a quantitative approach to the representation, classification, and generation of families of 3D (three-dimensional) particular discrete closed curves. Any 3D continuous curve can be digitalized and represented as a 3D discrete curve. Thus, a 3D discrete curve is composed of constant orthogonal straight-line segments. In order to represent 3D discrete curves, we use the orthogonal dir...

Many papers analyze the role of controllability and observability indices of normal linear systems in control theory and their use in the study of structural properties. This work introduces these indices for linear discrete-time descriptor systems. Such indices are studied in two different ways, by means of the state-space approach and using its transfer matrix . A canonical form of the state-...

Descriptor (singular) linear systems have been considered in many papers and books (Bru et al., 2003; 2002; Choundhury, 1972; Campbell et al., 1976; Dai, 1989; Guang-Ren Duan, 2010; Kaczorek, 2013; 2011a; 2014b; 2004; 1992; 2014c; 2011c; 2011d; 2011e; Virnik, 2008). The eigenvalue and invariant assignment by state and output feedbacks was investigated by Kaczorek (2004; 2011d), along with minim...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...

We present a novel method for a feature descriptor called an exact order based descriptor (EOD). The proposed method consists of three steps. First, to resolve ordering ambiguity for pixels of the same intensity, an exact order image is created by changing the discrete intensity into a k-dimensional continuous value. Second, exact order based features are generated globally and locally. Finally...

The positivity and asymptotic stability of the descriptor time‐varying discrete‐time linear systems are addressed. The Weierstrass‐Kronecker theorem on the decomposition of the regular pencil is extended to the time‐varying discrete‐time descriptor linear systems. Using the extension necessary and sufficient conditions for the positivity of the systems are established. Sufficien...