# Sparse Filtering Under Norm-Bounded Exogenous Disturbances Using Observers

## DOI:

https://doi.org/10.52846/stccj.2022.2.1.29## Keywords:

linear system, filtering, sparsity, exogenous disturbances, linear matrix inequalities, invariant ellipsoids## Abstract

The paper considers the sparse filtering problem under arbitrary norm-bounded exogenous disturbances. We propose a simple and universal observer-based approach to its solution, based on the LMI technique and the method of invariant ellipsoids; it allows the use of a reduced number of system outputs. From a technical point of view of application, we reduce the original problem to semi-definite programming, which is easily solved numerically. The proposed simple approach is easy to implement and can be equally extended to systems in continuous and discrete time.

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*Syst. Theor. Control Comput. J.*, vol. 2, no. 1, pp. 1–7, Jun. 2022, doi: 10.52846/stccj.2022.2.1.29.