We introduce a lacunary bivariate q-Laguerre-Sheffer family generated by the product of a Sheffer factor, a first q-exponential, and a q-Tricomi-Bessel kernel. The construction has three independent controls: the lacunarity index fixes which powers enter the finite sums, the kernel order changes the Bessel-type shifts, and the Sheffer factor supplies an additional deformation of the sequence. We derive explicit coefficient and convolution formulas, lowering relations, a quasi-monomial operator structure, a q-difference equation, and a q-translation identity. We then evaluate the polynomials at a mass-weighted graph Laplacian associated with heterogeneous network diffusion. This gives polynomial spectral filters whose vertex-domain support is limited to a prescribed graph-hop radius. Numerical examples illustrate the locality bound, spectral response tuning, comparison with a Chebyshev polynomial filter, kernel truncation accuracy, and a one-parameter calibration problem.
The event-triggered non-synchronous stabilization problem for Markov jump systems was investigated via state-feedback control. The possible mismatch between the plant and controller modes was modeled by a hidden Markov model. Both memoryless and memory-based switched event-triggered mechanisms were proposed to reduce the frequency of controller updates. Two sufficient conditions were established to guarantee the stochastic stability of the closed-loop system by employing Lyapunov-Krasovskii functionals, free-weighting matrices, and stochastic analysis. Computationally tractable schemes were then developed to obtain the state-feedback controller gains via congruence transformations. A numerical example is presented to illustrate the efficiency of the switched event-triggered non-synchronous state-feedback control schemes.
Synchronization in multilayer networks plays a fundamental role in many real-world systems; yet, understanding how interlayer structures influence synchronizability remains a major challenge. In this paper, we investigated the synchronizability of multilayer networks with undirected and directed interlayer couplings. By deriving the exact spectral properties of the corresponding supra-Laplacian matrices, explicit synchronizability criteria were established for bounded and unbounded synchronization regions. The results revealed that interlayer coupling patterns strongly affected synchronization behavior. In undirected multilayer networks, increasing the number of layers weakened synchronizability, whereas stronger intra-and interlayer coupling strengths could enhance synchronization performance. In contrast, multilayer networks with directed interlayer couplings exhibited different behavior: Synchronizability became independent of the number of layers, demonstrating the significant impact of coupling asymmetry on collective dynamics. Moreover, simulations on Erdo & uml;s-Renyi multilayer networks validated the theoretical predictions. These findings provide analytical insights into how multilayer architectures and coupling asymmetry shape synchronization dynamics and may offer guidance for the design and optimization of complex interconnected systems.
