Nonmonotonic Observer-Based Fuzzy Controller Designs for Discrete Time T-S Fuzzy Systems Via LMI

Abstract

In this paper, based on the nonmonotonic Lyapunov functions, a new less conservative state feedback controller synthesis method is proposed for a class of discrete time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. Parallel distributed compensation (PDC) state feedback is employed as the controller structure. Also, a T-S fuzzy observer is designed in a manner similar to state feedback controller design. The observer and the controller can be obtained separately and then combined together to form an output feedback controller by means of the Separation theorem. Both observer and controller are obtained via solving a sequence of linear matrix inequalities. Nonmonotonic Lyapunov method allows the design of controllers for the aforementioned systems where other methods fail. Illustrative examples are presented which show how the proposed method outperforms other methods such as common quadratic, piecewise or non quadratic Lyapunov functions.

Asynchronous fault detection observer design for discrete‐time piecewise linear systems

“…Therefore, new types of LFs, including fuzzy LFs and polynomial LFs, were later proposed in the literature to reduce such conservativeness. In recent years, many researchers have used the nonmonotonic LF methods in the field of control, such as, in which the nonmonotonic LFs with two sample variables in are established for the controller design of nonlinear systems, and in, the nonmonotonic decreasing of the LFs based on k sample variables is proposed to further reduce the conservatism of the methods in the works of Ahmadi and Parrilo and Derakhshan et al…”

“…Therefore, new types of LFs, including fuzzy LFs and polynomial LFs, were later proposed in the literature [24][25][26][27] to reduce such conservativeness. In recent years, many researchers have used the nonmonotonic LF methods in the field of control, such as, [28][29][30] in which the nonmonotonic LFs with two sample variables in 28,29 are established for the controller design of nonlinear systems, and in, 30 the nonmonotonic decreasing of the LFs based on k sample variables is proposed to further reduce the conservatism of the methods in the works of Ahmadi and Parrilo 28 and Derakhshan et al 29 Recently, a more general nonmonotonic LF consisting of common LFs was established in the work of Nasiri et al, 31 and the constructed method has been proven to provide better results than the existing LF approaches with k sample variables. However, it has been shown that using common LFs to ensure the stability of the system may be conservative in some cases.…”

Robust H∞ Filtering of Nonhomogeneous Markovian Jump Delay Systems via N‐Step‐Ahead Lyapunov‐Krasovskii Functional Approach

“…It has been successfully used for T-S fuzzy model to relax the monotonicity requirement of LF and further reduce the conservatism of the stability criteria, i.e., allowing the LF to increase locally during several sampling periods. Two-sample variation, i.e., ( +2 ) < ( ) [28][29][30], and -sample variation, i.e., ( + ) < ( ) [31][32][33][34][35][36][37], were fully developed for the T-S fuzzy model. Stability analysis and synthesis, robust ∞ controller design, observer-based fuzzy controller design, and output feedback stabilization have been intensively studied.…”

Delay-dependent stabilization condition for T-S fuzzy neutral systems

“…Through the modeling procedure, T-S fuzzy model can be described by fuzzy IF-THEN rules, which represents local linear input-output relations of a nonlinear model. In addition to fuzzy modeling scheme, the parallel distributed compensation (PDC) technique [5] is adopted to stabilize the overall T-S fuzzy model. For the stabilization condition analysis, Lyapunov direct method [6], [7] is mainly investigated to yield the stabilization conditions of T-S fuzzy model.…”