Sliding Mode Control Design for Linear Evolution Equations with Uncertain Measurements and Exogenous Perturbations

The paper studies the problem of sliding mode control design for linear evolution equations with incomplete and noisy measurements of the output and additive exogenous disturbances. The key result of the paper is an algorithm, generating an output-based feedback, which steers the state as close as possible to a given sliding hyperplane in a finite time. The optimality of the designed feedbacks is proven. The efficacy of the proposed algorithm is illustrated by a numerical example.