Abstract
ABSTRACT In this paper, the sparse feedback stabilisation in which the gain matrix has as many zero components as possible in linear delay systems is investigated. The necessary and sufficient condition for the asymptotic stability of the delay systems under sparse state feedback is given. By means of a special matrix norm and the transition matrix (fundamental matrix) of delay systems, the sparse gain matrix design problem is transformed into an optimisation problem. We further derive the proximal mapping of the special matrix norm, and then based on the gradient descent of the smooth part of the objective function, the proximal gradient method is introduced to develop an algorithm for solving the non-smooth optimisation problem. Numerical examples are given to illustrate the effectiveness of the proposed method.
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