The objective of the research is to develop a general method of constructing Lyapunov functions for non-linear non-autonomous differential inclusions described by ordinary differential equations with parameters. The goal has been attained through the following ideas and tools. First, three-point Poincare’s strategy of the investigation of differential equations and manifolds has been used. Seco...

The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the ...

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T -periodic logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T -periodic system with ti...

Group consensus problems of multi-agent systems in directed networks with fixed and switching topologies are addressed in this note. Under mild assumptions, necessary and/or sufficient conditions of group consensus are derived, based on algebraic graph theories and matrix theories. For the fixed topology case, the group consensus can be guaranteed by the Hurwitz stability of coefficient matrice...

The dynamical output feedback controller design for systems with distributed delay is concerned in this paper. Firstly, model transformation of the closed-loop system is used and a proper Lyapunov-Krsovskii functional is constructed, by which the stability criterion is obtained in terms of nonlinear matrices inequality, which guarantees the asymptotical stability of closed-loop system. Secondly...

This paper investigates the problem of adaptive stabilization of nonholonomic mobile robots with nonholonomic constraints under the condition that the kinematic parameters are unknown and no known constants can (lower and upper) bound them. By defining a new unknown parameter which need dynamic updating, and also by using input-state-scaling transformation and backstepping technique, an adaptiv...