The H∞ control problem for linear discrete-time descriptor systems which are of high index and possibly non-regular is considered. The goal is to compute a descriptor feedback such that the closed loop system is stable, causal, and H∞ norm bounded by a prescibed real number. In a recent solution of this problem, where causality is established by a preliminary feedback and where stability and H∞...

Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for the descriptor positive systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the minimum energy control problem are given. Procedure for computation o...

Robust stability is considered for uncertain discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov-Krasovskii functions (LKFs), which has been recently introduced in the continuous case, is applied: to a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the system with the perturbed delays and th...

Abstract. In this paper, we discuss stability properties of positive descriptor systems in the continuous-time as well as in the discrete-time case. We present characterisations of positivity and establish generalised stability criteria for the case of positive descriptor systems. We show that if the spectral projector onto the finite deflating subspace of the matrix pair (E, A) is nonnegative,...

In the sequel to [A. Ilchmann and V. Mehrmann, SIAM J. Control Optim., 44 (2005), pp. 1725–1747], we discuss a behavioral approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is “almost global” in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the “time axis” R\T, where T is a discrete...