Finite spectrum assignment problem for a differential system of neutral type

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

“…In a study [18], an approach was developed for assigning an arbitrary finite spectrum for linear systems with delays. Later, the finite spectrum assignment problem for time-delay systems by linear state feedback was studied in [19] for systems with one lumped delay in the states with the scalar controller, in [20] for systems with multiple commensurate lumped delays in the states with the scalar controller, in [21] for systems with multiple commensurate lumped delays in the states and control with the scalar controller, in [22] for systems with multiple commensurate lumped delays in the states and control with the multidimensional controller, in [23] for systems with multiple commensurate lumped and distributed delays in the states with the scalar controller, and in [24] for systems of neutral type with multiple commensurate lumped delays in the states with the scalar controller. In [25], the ACA problem was studied for single-input single-output (SISO) systems with commensurate lumped delays in the states by the dynamic output feedback controller.…”

Spectrum assignment and stabilization of linear differential equations with delay by static output feedback with delay

“…Here it is required to find conditions providing the desired placement of the spectrum of the system, that is, the sets of zeros of the characteristic function of the system. There are works on assignment of a given finite spectrum [10][11][12][13][14][15][16], spectral reducibility [17,18], i.e., reduction of systems to a finite (but not given) spectrum, modal controllability [19][20][21][22][23][24][25]. In the present paper, necessary and sufficient conditions are obtained for arbitrary spectrum assignability by linear static output feedback for a control system defined by a linear differential equation of n-th order with one lumped and one distributed delay in the state variable.…”

Finite spectrum assignment problem for bilinear systems with several delays

“…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]).…”

“…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].…”

“…One of the features that delay systems may possess is the presence of invariant eigenvalues that can be excluded from the spectrum only by using integral regulators [9]. Respectively, in general case, the closed-loop system becomes a system with lumped and distributed delays.…”