Synthesis of damping controllers for the solution of completely regular differential-algebraic delay systems

Finite spectrum assignment problem for bilinear systems with several delays

“…It follows from conditions (11) that the matrix (20) has the form (13). Taking into account (21), (19), (18), condition (10), and applying Lemma 1, we obtain that the system (1) is arbitrary finite spectrum assignable by constant control iff there exist u j ∈ K r j , j = 0, s, such that for all i = 1, n the following equalities hold:…”

“…The obvious corollary on stabilization follows from Theorem 1. Choosing the polynomial (18) in such a way that its roots belong to left half-plane ω η = {λ ∈ C : Re λ < −η < 0}, one can obtain exponential stability for the system (1) with any pregiven decay rate η > 0.…”

“…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]). They are also solvability conditions for the problem of assigning a finite spectrum [7,9].…”