On perturbing lyapunov functions

On quadratic Lyapunov functions

Φ0-stability of Impulsive Hybrid Setvalued Differential Equations with Delay by Perturbing Lyapunov Functions

The study of set differential equations has been initiated as an independent subject and several results of interest can be found in [4–5, 10–12, 14]. The interesting feature of the set differential equations is that the results obtained in this new framework become the corresponding results of ordinary differential equations as the Hukuhara derivative and the integral used in formulating the s...

Stability of Impulsive Hybrid Set-valued Differential Equations with Delay by Perturbing Lyapunov Functions

We study the stability of the zero solution of an impulsive set differential system with delay by means of the perturbing Lyapunov function method. Sufficient conditions for the stability of the zero solution of impulsive set differential equations with delay are presented.

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general...

On Lyapunov functions and data-driven dissipativity

Our contribution in this paper is twofold. In the first part, we study Lyapunov functions when a plant is interconnected with a dissipative stabilizing controller. In the second, we present results on data-driven approach to dissipative systems. In particular, we provide conditions under which an observed trajectory can be used to determine whether a system is dissipative with respect to a give...