Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays

Abstract

This paper studies the fuzzy filter design problem for signal estimation of nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of nonlinear discrete-time systems with time delays. Next, we design a stable fuzzy filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed index for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.

Distributed piecewise filtering design for large-scale networked nonlinear systems

“…It is noted that the common Lyapunov function proposed in [40] is not applicable to the distributed H ∞ filtering design for this case in this example. However, by applying Theorem 1, the feasible solutions of γ min = 3.9555 for the full-order filter and γ min = 6.5599 for the reduced-order filter are obtained, and the corresponding filter gains are Example 2.…”

“…The region index set is J i = {1, 2, 3}. Now, considering the case of full-order filter with a i = 0.9, the common Lyapunov function proposed in [40] is not applicable to the distributed H ∞ filtering design for this case in this example. However, by applying Theorem 1, the H ∞ filtering performance γ min = 3.3755 is obtained, and the obtained filter gains are Given the initial conditions x 1 (0) =[ 1.3, 0] T , x 2 (0) = [ 1.1, 0] T , and assume that the external disturbances satisfy w 1 (t) = 5e −0.02t sin(t) and w 2 (t) = 5e −0.02t cos(t), it is easy to see from Figs.…”

Analysis, Filtering, and Control for Takagi-Sugeno Fuzzy Models in Networked Systems

“…For example, the fuzzy ∞ filtering has been discussed in [50] for a class of nonlinear discrete-time systems with both multiple time-delays and unknown bounded disturbances. For the same kind of time-delays, in [51], a full-order ∞ filter has been designed to guarantee that the filtering error dynamics are stochastically stable and the given ∞ attenuation level is guaranteed.…”

Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems

“…Among different fuzzy models, the well-known Takagi-Sugeno (T-S) fuzzy model has attracted considerable research attention [1][2][3][4][5] and a large amount of literature has appeared on the fundamental issues of stability and stabilization for T-S fuzzy systems (see, e.g., [6,7] and the cited therein). Very recently, Choi et al [8] put forward a new method to formulate a framework that can describe T-S fuzzy systems with time-varying input delay and output constraints based on ( , , ) − -dissipativity, which not only synthesized ∞ control and passivity control, but also applied the obtained results to different road conditions.…”