Sparse feedback design in discrete-time 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 $\ell_1$-optimization theory. The efficiency of the approach is illustrated via numerical examples.