Improved filtering H∞ finite frequency of Takagi-Sugeno fuzzy systems

The work treats the filter H∞ finite frequency (FF) in Takagi-Sugeno (T-S) two dimensional (2-D) systems described by Fornasini-Marchesini local state-space (FM LSS)models. The goal of this work is to find an FF H∞ T-S fuzzy filter model design in such a way that the error system is stable and has a reduced FF H∞ performance over FF area swith noise is established as aprerequisite. Via the use of the generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions approach, Finsler’s lemma, and parameterize slack matrices, new design conditions guaranteeing the FF H∞ T-S fuzzy filter method of FM LSS models are developed by solving linear matrix inequalities (LMIs). At last, the simulation results are provided to show the effectiveness and the validity of the proposed FF T-S fuzzy of FM LSS models strategy by a practical application has been made.

Finite frequency H∞ control for wind turbine systems in T-S form

In this work, we study H_∞ control wind turbine fuzzy model for finite frequency(FF) interval. Less conservative results are obtained by using Finsler’s lemma technique, generalized Kalman Yakubovich Popov (gKYP), linear matrix inequality (LMI) approach and added several separate parameters, these conditions are given in terms of LMI which can be efficiently solved numerically for the problem that such fuzzy systems are admissible with H∞ disturbance attenuation level. The FF H∞ performance approach allows the state feedback command in a specific interval, the simulation example is given to validate our results.

Robust finite-time H∞ control of switched non-linear neutral systems in the presence of multiple disturbances using auxiliary matrices

This paper focuses on finite-time boundedness (FTB) of a class of switched non-linear neutral systems in the presence of multiple disturbances. Based on Lyapunov analysis, Finsler’s lemma and the average dwell-time concept, sufficient conditions are extracted to guarantee the FTB of the system. Using these sufficient conditions, finite-time ${H}_{\infty }$ controllers are designed via state feedback and static output feedback structures. The proposed controllers are less conservative than the existing Lyapunov-based approach and there are many degrees of freedom to achieve feasible linear matrix inequalities. Finally, two examples are simulated to validate the proposed approach and to show that the obtained theoretical results are less conservative than the existing papers.

New Decentralized Control of Interconnected Systems

In this paper, we present a new decentralized H∞ control for interconnected systems, the interconnected system consists of several subsystems. The proposed approach based on Lyapunov functional and a H∞ criterion, employed to reduce the effect of interconnections between subsystems. In the first, we study the stability of the global system in closed loop using a criterion H∞, the stability conditions are presented in terms of LMI. In the second, to improve this approach, a Finsler’s lemma is used for the stability analysis by LMIs. Some sufficient conditions, ensuring all the closed-loop stability are supplied in terms of Linear Matrix Inequalities (LMIs), and the new feedback gain matrix of each local controller is obtained by solving the LMIs. Finally, the practice examples are given to illustrate the efficiency of the present method

Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0<α<1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler’s Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.