Criteria for Modal Controllability of Completely Regular Differential-Algebraic Systems with Aftereffect

Finite spectrum assignment problem for bilinear systems with several delays

“…Next, by 7, we have Γ j = Γ 0 , j = 1, s. Hence, if rank Γ 0 = n, then rank Γ j = n, i.e., the matrices Γ j (j = 1, s) have the full rank. Hence, rank ∆ j = n, j = 1, s, i.e., condition (17) holds. Thus, if the system (1) has the form 5…”

“…Then the system (31) is arbitrary n-point spectrum assignable by constant control iff conditions (16), (17) hold.…”

“…Suppose that the matrices of the system (31) have the special form (10), (11). Suppose conditions (16), (17) hold. Then the system (31) is exponentially stabilizable by constant control with an arbitrary pregiven decay rate.…”

“…Suppose that the matrices of the system (31) have the special form (10), (11). Suppose that the truncated system (33) is consistent, and condition (17) holds. Then the system (31) is arbitrary n-point spectrum assignable by constant control.…”

“…To date, a fairly large number of studies have been devoted to the problems of spectrum control and stabilization of delayed systems, which have already become classic. These are works on stabilization of an object with delay [1][2][3][4][5], stabilization of a group of objects by a single controller [6], assignment of a given finite spectrum [7][8][9], spectral reducibility [10][11][12], i.e., reduction of systems to a finite (but not given) spectrum, modal controllability [13][14][15][16][17]. At present, for retarded and neutral type systems, as well as for completely regular differential-algebraic systems with several delays, spectral criteria of modal controllability have been obtained [13,15,16] that coincide in form with the criterion of complete controllability (see, for example, [18]).…”