State Estimation for Fractional-Order Complex Dynamical Networks with Linear Fractional Parametric Uncertainty

This paper deals with state estimation problem for a class of fractional-order complex dynamical networks with parametric uncertainty. The parametric uncertainty is assumed to be of linear fractional form. Firstly, based on the properties of Kronecker product and the stability of fractional-order system, a sufficient condition is derived for robust asymptotic stability of linear fractional-order augmented system. Secondly, state estimation problem is then studied for the same fractional-order complex networks, where the purpose is to design a state estimator to estimate the network state through available output measurement, the existence conditions of designing state estimator are derived using matrix's singular value decomposition and LMI techniques. These conditions are in the form of linear matrix inequalities which can be readily solved by applying the LMI toolbox. Finally, two numerical examples are provided to demonstrate the validity of our approach

LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods