Conditions for D-stability of discrete singular systems with time-delays

The paper first discusses the D-pole placement problem of discrete-time singular systems with multiple time-delays. Two D-stability criteria are proposed to ensure that all the generalized eigenvalues of discrete-time singular systems with multiple time-delays are located inside a specific disk D(α,s) centered at (α,0) with radius S. One is a direct judgment (i.e., test l<1), and the other is a boundary test. These criteria are easy test, and convenient for the application in the engineering. When D(α,s) is a unit circle, the proposed criteria will become the asymptotic stability criteria. An example is given to illustrate the practicality of the obtained result