Robust Sparse Filtering Under Bounded Exogenous Disturbances

An approach to the solution of a robust sparse filtering problem via use of a reduced number of outputs under arbitrary bounded external disturbances and norm-bounded system uncertainties using an observer is proposed. The approach is based on the LMI technique and the method of invariant ellipsoids, and made it possible to reduce the initial problem to parameterized semidefinite programming that can be easily solved numerically. Two ways to control sparsity are proposed: controlled relaxation approach and Pareto frontier approach.