This paper deals with a state feedback H∞ control problem for linear time-invariant discrete-time descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma (BRL) is extended on the class of uncertain descriptor systems. The control design procedure based on the conditions of BRL for uncertain descriptor systems is proposed. Numerical example is included to i...

Linear periodic descriptor systems represent a broad class of time evolutionary processes in micro-electronics and circuit simulation. In this paper, we consider discrete-time linear periodic descriptor systems and study the concepts of periodic reachability and observability Gramians. We also discuss a lifted representation of periodic descriptor systems and propose a balanced truncation model...

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

We investigate the numerical solution of a descriptor type discrete–time Riccati equation and give its main applications in several key problems in robust control formulated under very general hypotheses: rank compression (squaring down) of improper or polynomial systems with L∞–norm preservation, (J, J ′)–spectral and (J, J ′)–lossless factorizations of a completely general discrete–time syste...

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

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...

— This paper considers the H∞ control problem for a general discrete–time system, possibly improper or polynomial. The parametrization of suboptimal H∞ output feedback controllers is presented in a realization–based setting, and it is given in terms of two descriptor Riccati equations. Moreover, the solution features the same elegant simplicity of the proper case. An interesting numerical examp...