A new parameter-dependent approach to robust energy-to-peak filter design

This paper presents a new parameter-dependent approach to the design of robust energy-to-peak filters for linear uncertain systems. Given a system containing polytopic parameter uncertainties, our purpose is to design a robust filter such that the filtering error system is asymptotically stable with a guaranteed L₂-L_∞ disturbance attenuation level γ. This problem is solved by introducing new energy-to-peak performance characterizations, and by utilizing an idea of structured parameter-dependent matrices. New sufficient conditions are obtained for the existence of desired filters in terms of linear matrix inequalities, which can be easily tested by using standard numerical software. If these conditions are satisfied, a desired filter can be readily constructed. Both continuous- and discrete-time systems are considered, and the effectiveness and advantages of the proposed filter design methods are shown via two numerical examples.