Robust ℒ2 – ℒ℞ filtering of uncertain systems

The paper addresses the problem of robust ℒ₂ - ℒ_∞ filter design for affine uncertain systems. The robust ℒ₂ - ℒ_∞ Luenberger-type filters are designed based on the solution of a set of linear matrix inequalities. Parameter-dependent Lyapunov functions are employed for filter design with the objective of minimizing the worst-case peak value of the filtering error output signal over all bounded energy disturbance inputs while the filtering error system remains affinely quadratically stable. To determine the robust filter gain matrix, first we obtain the analysis conditions that enable us to calculate the ℒ₂ - ℒ_∞ gain performance of such systems in terms of LMIs. Then, the synthesis conditions to provide the robust filter are obtained. Comparative examples are finally presented to validate the methodology and to demonstrate the advantages of the proposed techniques relative to the past approaches.