Observer-based H_∞ control with finite frequency specifications for discrete-time T–S fuzzy systems

observer–controller synthesis approach in low frequency for T–S fuzzy systems

“…□ Remark 5 The method in [47] is a two‐step method to recursively solve the BMI form stability conditions. On the contrary, the conditions in Theorem 2 is in LMI form, which can be directly solved by the convex optimisation approach. Remark 6 For the observer–controller design of the discrete fuzzy system in finite frequency [48], Rachid first proposed the ‘one‐step’ stability analysis method, different from this approach, and to the best of the authors' knowledge, the ‘one‐step’ stability analysis technique is first proposed in Theorem 2 for the continuous case. Remark 7 After solving the gain matrices from Theorem 2. The satisfaction of Assumption 1 should be double checked with the observer–controller gain and .…”

“…For the observer–controller approach of linear systems in finite frequency, ‘two‐step’ methods for solving the stability conditions of active fault tolerant control are proposed in [46, 47]. For discrete‐time T–S fuzzy systems, the problem of observer‐based control in the finite frequency domain is investigated in [48]. However, to the best of the authors' knowledge, there exist very few results about the observer–controller synthesis by ‘one‐step’ methods for continuous‐time T–S fuzzy systems, which motivates our work.…”

Robust finite frequency H∞ control for Lipschitz nonlinear systems

“…Indeed, the feasibility of the approach has been extended and various kinds of systems have been investigated by researchers. For example, various H ∞ control methods for T-S fuzzy systems in finite-frequency domain were presented in Rachid et al (2018), Wang and Yang (2016) and Wang et al (2013). Some studies were devoted to the finite-frequency control design for delayed systems (Dong and Yang, 2018; Tao et al, 2019; Xu et al, 2017).…”

Novel robust observer‐controller synthesis method for Takagi‐Sugeno systems

“…Homogeneous polynomially parameter‐dependent methods are given by [35,36]. In [37], robustness and stability conditions in finite frequency are listed. In addition, membership‐function‐dependent approach stability conditions are investigated in [38].…”