Abstract
We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.
Highlights
IntroductionA large number of works have been devoted to the problem of stability of time-delay systems and problems of stabilization for control systems with delays (see reviews [1,2,3,4])
A large number of works have been devoted to the problem of stability of time-delay systems and problems of stabilization for control systems with delays.A number of methods have been developed to solve this problem
Consider a control system defined by a linear differential equation of nth order where the input is a linear combination of m variables and its derivatives of order ≤ n − p, and the output is a k-dimensional vector of linear combinations of the state x and its derivatives of order ≤ p − 1 (1 ≤ p ≤ n): x(n) + a1x(n−1) + . . . + anx =
Summary
A large number of works have been devoted to the problem of stability of time-delay systems and problems of stabilization for control systems with delays (see reviews [1,2,3,4]). The problem of spectrum assignment by static output feedback (for systems without delays) is as follows: consider a linear time-invariant control system x = Fx + Gu, y = Hx,. The problems of stabilization and spectrum assignment by static output feedback for time-delay systems are more difficult to study. Another study [40] considered the output feedback stabilization problem for a class of linear SISO systems with I/O network delays. The problem of stabilization of linear time-varying systems with input delays via delayed static output feedback is studied in [41]. We extend Theorem 1 on arbitrary coefficient assignment by static output feedback to systems with non-commensurate lumped and distributed delays in the state variable.
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