This study investigates the problem of robust stability in a class of switched interconnected systems that involve unstable modes, time-varying and continuously distributed state delays, as well as uncertainties in switching signal and system parameters. Switching uncertainties lead to fluctuations in both the prescribed switching instants and the nominal switching sequence, which significantly affect system stability. To address these challenges, two novel concepts are introduced: the composite switching signal and the generalized nominal switching signal. Additionally, a new index, referred to as the generalized mode-changing rate, is proposed. By utilizing these concepts and the new index, the average dwell time approach and the vector Lyapunov function method are integrated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to illustrate the effectiveness and applicability of the proposed theory.

In recent years, the peer-to-peer (P2P) educational information sharing system was modeled by a system of fuzzy relation inequalities (FRIs) with addition-min or max-min composition. The max-min FRIs system was applicable to the P2P network considering the highest download traffic among the terminals. Moreover, every solution to such a max-min FRIs system corresponds exactly to one feasible flow control scheme. To embody the stability of a given feasible scheme, we introduce the concept of the widest symmetrical interval solution (WSIS), regarding the corresponding solution in the max-min FRIs system. Some effective procedures are proposed to find the WSIS regarding a provided solution. In addition, aiming to find the most stable feasible scheme, we further define the concept of a centralized solution. Some effective procedures are also proposed to find the centralized solution regarding the max-min FRIs system. Some numerical examples are provided, respectively, to demonstrate our proposed resolution procedures. Our obtained centralized solution will provide decision support for system administrators considering the stability of the feasible scheme.

In a supply chain system, the price of the goods should satisfy some requirements of the consumer. These requirements have been exactly characterized by a group of min-product fuzzy relation inequalities (FRIs). Correspondingly, any feasible pricing scheme is characterized by a solution of the min-product FRIs system. For a given pricing scheme, or say a given solution in the min-product FRIs, the flexibility is reflected by the maximum amplitude, or equivalently the maximum amplitude interval solution (MAIS). Motivated by such an application background, this work attempts to study the MAIS in min-product FRIs. An efficient algorithm is discovered for computing the MAIS of a solution within the given min-product system. The MAIS will help the system manager be aware of the flexibility of a given pricing scheme and produce better decision-making.

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.