Unknown input observer design for Takagi-Sugeno fuzzy stochastic system

Abstract

This paper deals with the unknown input observer design for Takagi-Sugeno (T-S) fuzzy models subjected to measurement noise and stochastic noise. The method applies the singular system theory by considering the measurement noise as an augmented system state, and then an unknown input observer based on the techniques of singular systems is developed to estimate both the system states and measurement noise simultaneously. Under a necessary assumption, the error dynamic system of the observer is free from the unknown inputs. And the observer gain matrix is determined by means of minimum covariance matrix of state residual. Two simulation examples are given to illustrate the correctness and effectiveness of the proposed method.

Decentralized Polynomial Observer Design for Discrete‐Time Large‐Scale Polynomial T‐S Fuzzy System

“…The rank conditions of matrices and in Assumption 1 are necessary to guarantee the existence of the general solution of matrix equation in the consequent section. This is a common condition that can be found in many previous papers studying about unknown input method such as [30][31][32][33][34].…”

“…Moreover, with the proposed method, the interconnection terms do not need to linearize to transform them under the T-S fuzzy model form [21,[26][27][28][29], which assists to avoid increasing of the fuzzy rules and complexity of the modeled system. The unknown input method [30][31][32][33][34] is employed to design observer for the largescale polynomial T-S fuzzy system in which the effects of the interconnection terms are eliminated completely and unmeasurable states are estimated asymptotically.…”

Sliding mode control for uncertain T-S fuzzy systems with input and state delays

“…In [9,21], the authors deal with the design of a class of sliding mode observers with time delay. In [5], the authors deal with the unknown input observer design for T-S fuzzy models subjected to measurement noise and stochastic noise. In [1], the authors propose an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay.…”

State estimation and simultaneous unknown input and measurement noise reconstruction based on adaptive H ∞ observer

“…In comparison, we have checked that the observer matching condition, which is crucial in the designs proposed in [24,25], is not satisfied for this example, so the discontinuous control terms (32) and (9) in [24,25], respectively, cannot be implemented. Fig.…”

“…Hence, unknown input observer designs can be found their applications in many fields, including fault-tolerant control design, fault diagnosis and isolation, and chaos synchronization-based secure communication [6,7]. Recently, many results on unknown input observer designs can be found in literatures [8][9][10][11][12][13][14][15][16][17][18][19][20].…”