This paper proposes a new approach for the analysis of consensus of multi-agent systems subject to time-varying delayed control inputs and switching topology. The main contribution is a condition for consensus for a networked system based on linear matrix inequalities that takes into account the joint effect of time-varying delays and switching network topology. Topology changes are modeled using Markov jumps with uncertain rates of transitions. A practical example is shown to illustrate the main result in various scenarios.

Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed. The key idea is to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions. By relying on these special local transformations, the associated linear matrix inequalities that are used to prove the system's stability can be relaxed without increasing the number of conditions. In addition, to enhance the usefulness of the proposed methodology, one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives. A standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases.

In this paper, the stability analysis and control design of Takagi-Sugeno (TS) fuzzy systems subject to uncertain time-delay are addressed. The proposed approach is based on linear matrix inequalities and the Lyapunov-Krasovskii theory, where a new fuzzy weighting-dependent Lyapunov-Krasovskii functional is introduced. By employing the Gu discretization technique and strategies to add slack matrix variables, less conservative conditions are obtained. Numerical experiments are performed to illustrate the effectiveness of the proposed methodology.