This article deals with the design of quadratic and linear dynamic output feedback controllers for systems to ensure, on one hand, local exponential stability origin in closed-loop form and, other increase an estimate basin attraction as large possible. The introduction a term controller allows us consider same class dynamics studied system. Here, our approach is Lyapunov function respect exten...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete–time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi–global practical Lyapunov functions for globally asymptotica...

Asymptotic behavior of a partial state of coupled nonautonomous ordinary and/or partial differential equations is investigated. The system assumes the existence and uniqueness of the solution and the existence of a Lyapunov function candidate. Although ordinary Lyapunov analysis can not guarantee the asymptotic convergence of the state, the analysis in this paper assures the asymptotic converge...

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related t...

This paper discusses the discrete analogue of the gradient of a function and shows how discrete gradients can be used in the numerical integration of ordinary diieren-tial equations (ODE's). Given an ODE and one or more rst integrals (i.e., constants of the motion) and/or Lyapunov functions, it is shown that the ODE can be rewritten as a `linear-gradient system.' Discrete gradients are used to ...