The Lyapunov function plays an important role in the stability theory of dynamical systems. Its counterpart for discrete systems is not studied so much, though importance such increasing. In this letter, attempt made to construct a analog competitive Lotka-Volterra equation. For purpose, logarithmic defined and its effectiveness shown.

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead ...

Parameterized Lyapunov bounds and shifted quadratic guaranteed cost bounds are merged to develop shifted parameter-dependent quadratic cost bounds for robust stability and robust performance. Robust fixed-order (i.e., fulland reduced-order) controllers are developed based on new shifted parameter-dependent bounding functions. A numerical example is presented to demonstrate the effectiveness of ...

Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed. We consider parameterized families of discrete-time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete-time model is used to design a controller for...

In this paper we consider parameterized Lyapunov inequalities arising in stability analysis of discrete-discrete and continuous-discrete 2D systems. A necessary condition for their feasibility is presented. This condition is based on an optimization method published earlier by the author. Its properties include being reasonably easy to check, and its coverage being adjustable via the algorithm’...

The stability problem on delay-dependent exponential convergence for neutral-type systems with nonlinear perturbations is investigated in this paper. A linear matrix inequality (LMI) based exponential stability criterion is derived by means of the Lyapunov-Krasovskii functional approach and a parameterized model transformation technique. An example is used to illustrate the less conservative re...

This paper proposes a general multiscroll Lorenz system family by introducing a novel parameterized nth-order polynomial transformation. Some basic dynamical behaviors of this general multiscroll Lorenz system family are then investigated, including bifurcations, maximum Lyapunov exponents, and parameters regions. Furthermore, the general multiscroll Lorenz attractors are physically verified by...

Abstract This is the second part of our study on dimension theory $C^1$ iterated function systems (IFSs) and repellers $\mathbb {R}^d$ . In first [D.-J. Feng K. Simon. Dimension estimates for repellers. Part I. Preprint , 2020, arXiv:2007.15320], we proved that upper box-counting attractor every IFS ${\Bbb R}^d$ bounded above by its singularity dimension, packing ergodic invariant measure assoc...