There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems

H∞ model reduction for T-S fuzzy systems over finite frequency ranges

This paper investigates the design problem of robust H∞ filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing an H∞ performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence of H∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results.

Robust H∞ filtering for 2D continuous systems with finite frequency specifications

This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov–Krasovski functional combined with Finsler’s lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.

New Relaxed Stability Conditions for Uncertain Two-Dimensional Discrete Systems

This paper considers the H∞ filtering for nonlinear discrete-time systems in the Takagi-Sugeno (T-S) fuzzy model. The approach is based on the fuzzy filters in Finite Frequency (FF) domain. The objective is to propose a new design with sufficient condition via LMI formulations. Less conservative results are obtained by introducing slack matrices. This method provides extra degree of freedom in optimization of the H∞ performance. Three fuzzy filters are designed to deal with noises in Low-, Middle- and High-Frequency domain (LF,MF,HF), respectively. The efficiency of the proposed approach is shown be an example.

H∞ filtering of T-S fuzzy systems in Finite Frequency domain

This paper deals with $$H_{\infty }$$
 filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman–Yakubovich–Popov lemma, polynomially parameter-dependent Lyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition is obtained for analyzing the $$H_{\infty }$$
 performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed $$H_{\infty }$$
 filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method.

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Robust $$H_{\infty }$$ H ∞ Filters for Uncertain Systems with Finite Frequency Specifications

This paper examines the design problem H∞ of the reduced order model for two-dimensional (2D) discrete systems described by the Roesser model with a control input assumed to operate in a finite frequency (FF) domain. Given an asymptotically stable system; our goal is to find a stable reduced order system so that the error of the transfer functions between the original system and the reduced order is limited to a range FF. Using the well-known generalized lemma of Kalman Yakubovich Popov (gKYP) and the Finsler's lemma, sufficient conditions for the existence of the reduction of the H∞ model for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). An illustrative example is provided to show the utility and potential of the proposed results.

Abderrahim El-Amrani

Papers

H∞ model reduction for T-S fuzzy systems over finite frequency ranges

Robust H∞ filtering for 2D continuous systems with finite frequency specifications

H∞ filtering of T-S fuzzy systems in Finite Frequency domain

Robust $$H_{\infty }$$ H ∞ Filters for Uncertain Systems with Finite Frequency Specifications

H∞ Model Reduction for Two-Dimensional Discrete Systems in Finite Frequency Ranges