Simultaneous Estimation of State and Unknown Input With $l_{\infty}$ Guarantee on Error-Bounds for Fuzzy Descriptor Systems

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

“…The singular redundancy representation has been exploited for control and observer designs of TS fuzzy descriptor systems with linear consequents. 23,36,48 However, fuzzy observer design using the N-TS fuzzy form (7) has not yet been reported in the open literature. This singular model reformulation allows for an effective treatment of the nonlinear descriptor matrix (x k ) in (1), especially in the context of TS fuzzy observer design with unmeasured premise variables.…”

“…where 𝒱 k is defined in (23), and Δ𝒱 k = 𝒱 k+1 − 𝒱 k is its difference along the trajectory of the error dynamics (17). It follows from ( 27) that…”

“…The positive scalar 𝜖 and the MF-dependent matrix H(h) are introduced in the descriptor observer design through equality (25) to reduce the conservatism. This null-term relaxation approach has been effectively exploited for TS fuzzy-model-based control and observer design, see for instance References [23,57].…”

“…10 Then, the goal focuses on reducing the design conservatism via the use of various Lyapunov candidate functions and/or relaxation techniques. 23 However, assuming that all the premise variables can be measured from sensors, the TS fuzzy observer design in Category 1 can only be applied to a restrictive class of nonlinear systems. To overcome this drawback, research attention has been paid to the TS fuzzy observer design in Category 2.…”

“…Various extensions have been proposed to LPV descriptor systems, [41][42][43] and TS fuzzy descriptor systems. 21,23,36,44,45 However, dealing with the descriptor forms in LPV and/or TS fuzzy observer designs still remains a major challenge. Indeed, most of existing results can only be applied to systems with a linear descriptor matrix.…”