Finite spectrum assignment problem in linear systems with state delay by static output feedback

Finite spectrum assignment problem for bilinear systems with several delays

“…Taking into account that det G = 1 = 0, we see that the system (28) is resolvable with respect to u 0 (over K) for any pregiven γ i ∈ K, i = 1, n, iff condition (16) Remark 1. Let us show that Theorem 1 is a generalization of [29,Theorem 2]. Suppose that the system (1) has the form (5), i.e., the equalities (6), (7), (8) are fulfilled.…”

“…Suppose that the system (1) has the form (5), i.e., the equalities (6), (7), (8) are fulfilled. Suppose that the matrices of the system (5) (i.e., of the system (2.4) of [29]) have the form (1.6), (1.7), (2.5) of [29], that is the matrix A has the lower Hessenberg form with nonzero superdiagonal entries (i.e., the form (10)), the first p − 1 rows of the matrix B and the last n − p rows of the matrix C are equal to zero, and P j (j = 1, s) have the form (11). Then the matrices (6), (7) will satisfy the form (10), (11).…”

“…Then the matrices (6), (7) will satisfy the form (10), (11). Next, the condition 1 of [29,Theorem 2], which states that, for the system (5), the matrices C * B, C * AB, . .…”

“…In [29] the following linear stationary differential control system with several noncommensurate delays was considered:…”

“…x ∈ K n is a state vector, w ∈ K m is an input vector, and y ∈ K k is an output vector. For the system (2), (3) in [29] the controller is constructed as linear static output feedback with delays…”