This paper studies the consensus problem of nonlinear leader-following multi-agent systems (MAS). To do this, the error dynamics between the leader agent and follower ones are described via a Takagi-Sugeno (TS) fuzzy model. If the obtained TS fuzzy model is stable, then all of the nonlinear agents reach consensus. The consensus problem is investigated based on the parameterized or fuzzy Lyapunov function combined with a technique of introducing slack matrices. The slack matrices cause to decouple the Lyapunov matrices from systems ones and therefore, sufficient consensus conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed slack matrices add an extra degree-of-freedom to the LMI conditions and also decrease the conservativeness of the LMI-based conditions. Finally, in order to illustrate the effectiveness and merits of the proposed method, a numerical example for the consensus problem of nonlinear leader-follower MAS with thirteen followers is solved.

This paper presents a modified method for approximating systems by a sequence of ‎linear time varying systems. The convergence proof is outlined and the potential of ‎this methodology is discussed. Simulation results are used to show the effectiveness ‎of the proposed method‏.‏

In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and so the parameterized system of equations appears. This work considers the parameterized Sylvester matrix equations and tries to propose some methods containing a direct method and two iterative methods to obtain outer estimations of the solution set.

In this paper, a general complex fuzzy linear system is introduced and a numerical procedure for calculating solution is proposed. Finally, some numerical examples are given to illustrate the mentioned method.

As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication. Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the inner point of supports, of fully fuzzy linear systems (shown as FFLS) is proposed, if they exist by an analytic approach. The system's parameters were splitted into two groups of nonpositive and nonnegative by solving a multi objective linear programming problem, MOLP, and employing an embedding method to transform n×n FFLS to 2n×2 n parametric form linear system and hence, transforming operations on fuzzy numbers to operations on functions. And finally, numerical examples are used to illustrate this approach.

The Index Generalized Minimal RESidual (IGMRES) algorithm is designed to compute the Drazin-inverse solution of a linear system of equations $Ax=b$, where $A$ is an arbitrary square matrix with index $\gamma$. If $\gamma=0$, then the this method method coincide with Generalized Minimal RESidual (GMRES) method. Also, the {$k^{th}$} ideal index generalized minimal residual polynomial of $A$ is introduced and the roots of these polynomials are studied. Moreover, by numerical results the convergence rate of these methods are compared by two examples.