A Finite Frequency Approach to H_∞ Filtering for T–S Fuzzy Systems with Unknown Inputs

Abstract

This paper deals with the problem of state estimation of T-S fuzzy systems subject to unknown inputs. The proposed observer is designed in finite frequency domain to reduce the conservatism generated by those designed in the entire frequency domain when the unknown input frequency ranges are known beforehand. First, a finite frequency H ∞ index is introduced to measure the robustness against unknown inputs. Then, design conditions are derived in linear matrix inequality terms. Finally, an illustrative example is introduced to check the developed methodology.

Improved Input and State Estimation for Linear Stochastic Systems with Direct Feedthrough

“…If the input dynamic equation is exactly known, a common approach to solve this problem is the augmented state-space method (ASM) which treating x k and d k as the augmented state [30]. However, the augmented state-space method does not suit for this situation because equations (9) and (10) are not always exact, they just describe the boundedness of the change of unknown input vector. Moreover, the estimation accuracy of ASM is not always satisfied, especially when the unknown input changes abruptly.…”

“…The comparison simulation results are shown in Fig. 3 in Section V. Now, based on the recursive filter (4)-(8) and equations (9) and (10), the improved recursive filter can be designed as follows.…”

H∞ Filtering for Spatially Interconnected Time‐Delay Systems with Interconnected Chains in Finite Frequency Domains

“…whereP,Z,Ξ, Θ and Σ are defined as in (19) withQ = 0. Moreover, if the previous conditions are satisfied, the filter ( f ) is given by (21).…”

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

“…Zhang et al (2015); Chang et al (2014); Zhai et al (2018) and the reference therein. Chibani et al (2016) proposes a finite-frequency unknown input observer design method for T-S fuzzy systems. This method is further extended to fault detection in Chibani et al (2017).…”