Automation and Remote Control

, Volume 79, Issue 7, pp 1175–1190 | Cite as

Sparse Feedback Design in Discrete-Time Linear Systems

  • A. V. BykovEmail author
  • P. S. Shcherbakov
Linear Systems


The subject of this paper is the analysis of sparse state feedback design procedures for linear discrete-time systems. By sparsity we mean the presence of zero rows in the gain matrix; this requirement is natural in the engineering practice when designing “economy” control systems which make use of a small amount of control inputs. Apart from the design of stabilizing sparse controllers, the linear-quadratic regulation problem is considered in the sparse formulation. Also, we consider a regularization scheme typical to the ℓ1-optimization theory. The efficiency of the approach is illustrated via numerical examples.


linear discrete-time systems sparse feedback convex approximation linear-quadratic regulation regularization 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.UCHi.RUMoscowRussia
  2. 2.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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