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-...

<p style='text-indent:20px;'>In this paper, an optimal control model ruled by a class of linear discrete-time stochastic descriptor systems is considered under quadratic index performance. Employing dynamic programming method, recurrence equation to simplify the problem presented provided that are both regular and impulse-free. When objective function quadratic, according equation, linear...

We consider the (sub)optimal H∞-control problem for discrete time descriptor systems. Necessary and su cient optimality conditions are derived in terms of de ating subspaces of palindromic matrix pencils. This approach allows the use of structure preserving matrix techniques which lead to a more robust method compared with currently used algorithms. The approach is suitable for standard systems...

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 paper considers a robust decentralized H∞ control problem for uncertain multi-channel discrete-time descriptor systems with time-delay. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in the system, time-delay and output matrices. Our interest is focused on dynamic output feedback. A sufficient condition for the uncertain multi-channel discrete-time descriptor s...

For discrete-time descriptor syslems, various generalized Lyapunov equations were studied in the literature. Howevn these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for disc...

In this paper, we establish a model reduction technique for periodic discrete-time descriptor systems exploiting the generalized inverses of the periodic singular matrix pairs associated with the systems. We compute the generalized inverses of periodic singular matrix pairs to implement a structure preserving iterative method for the solution of the periodic projected Lyapunov equations that ar...