Filter design for discrete-time two-dimensional T–S fuzzy systems with finite frequency specification

ABSTRACT

This paper deals with the filter design problem of two-dimensional (2-D) discrete-time nonlinear systems described by Fornasini–Marchesini local state–space (FM LSS) model under Takagi–Sugeno (T–S) fuzzy rules. The frequency of disturbance input is assumed to be known and to reside in a finite frequency (FF) range. A novel so-called FF $l_2$ gain is defined for 2-D discrete-time systems, which extends the standard $l_2$ gain. The aim of this paper is to design filters such that the filtering error system is asymptotically stable and has the disturbance attenuation performance in sense of FF $l_2$ gain. Sufficient conditions for the existence of a desired fuzzy filter are established in terms of linear matrix inequalities (LMIs). Simulation examples demonstrate the technique and its advantage.

Keywords:

• 2-D discrete-time systems
• T–S fuzzy systems
• finite frequency
• $l_2$ gain
• filter design

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Zhou  http://orcid.org/0000-0002-2907-7269

Additional information

Funding

This work was supported jointly by the National Natural Science Foundation of China under Grant Nos. 61703137 and 61573001, and the Fundamental Research Funds for the Central Universities under Grant No. 2019B14814.