An LMI-Based Proportional-Derivative Observer for Singular Linear Systems

This paper proposes a solution to design an observer for singular linear systems in terms of linear matrix inequalities whose solvability is verified in polynomial time. The observer under design shares the idea of a Luenberger one but adding the derivative of the outputs, which leads to the regularization of the error system. The direct Lyapunov method is employed for designing both the proportional and derivative gains and thus guaranteeing the stability of the error system. Two examples illustrate the effectiveness of the proposal.