Filter Design for Interval Type-2 Fuzzy Systems With <italic>D</italic> Stability Constraints Under a Unified Frame

Abstract

This paper investigates the problem of filter design for interval type-2 (IT2) fuzzy systems with D stability constraints based on a new performance index. Attention is focused on solving the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , passive, and dissipativity fuzzy filter design problems for IT2 fuzzy systems with D stability constraints in a unified frame. Under the new performance index frame, using Lyapunov stability theory, a novel type of IT2 filter is designed such that the filtering error system guarantees the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , passive, and dissipativity performance levels with D stability constraints. The existence condition of the IT2 filter is expressed as the convex optimization problem, and the filter parameters in the condition can be solved by the standard software. The IT2 fuzzy model and IT2 fuzzy filter do not need to share the same lower and upper membership functions. Finally, a numerical example is provided to show the effectiveness of the proposed results.