We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease condi...

This paper presents a new nite-dimensional linear matrix inequality (LMI) formulation for the induced L2-norm synthesis of linear parameter-varying (LPV) systems. The approach is based on a nonsmooth dissipative systems theory using a continuous, quasi-piecewise a ne parameter-dependent Lyapunov function. The new method is less conservative than previously published techniques based on either a...

This paper deals with the analysis and design of the state feedback fuzzy controller for a class of discrete time Takagi -Sugeno (T-S) fuzzy uncertain systems. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequality (LMI) formalism. The main goal is to reduce the conservatism of the stabilization conditions using some particular Lyapunov functions. Four nonqu...

This report presents first steps at applying chaos theory to the solar activity cycle. We provide brief reviews of the history of sunspot records, the mathematical framework of chaos theory, and solar dynamo theory. Finally, we present results of nonlinear analysis of solar motion and propose that further research focus on characterizing local Lyapunov exponents of solar dynamics.

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabiliza...

Closed physical systems eventually come to rest, the reason being that due to friction of some kind they continuously lose energy. The mathematical extension of this principle is the concept of a Lyapunov function. A Lyapunov function for a dynamical system, of which the dynamics are modelled by an ordinary differential equation (ODE), is a function that is decreasing along any trajectory of th...

Semiquantitative simulation is a novel approach for the analysis of uncertain dynamic systems that performs a comprehensive simulation study based on automated reasoning methods (for example with the SQSIM algorithm). Semiquantitative simulation of complex models is, however, hindered by the limited automated reasoning capabilities of the currently available semiquantitative simulation techniqu...

This research work investigates the global chaos synchronization of identical chaotic systems based on sliding mode control theory and Lyapunov stability theory. The paper begins with a problem statement on global chaos synchronization of chaotic systems. A general result is derived for the global chaos synchronization of chaotic systems using slide mode control and this result is established u...

A family of time-varying hyperbolic systems of balance laws is considered. The partial differential equations of this family can be stabilized by selecting suitable boundary conditions. For the stabilized systems, the classical technique of construction of Lyapunov functions provides a function which is a weak Lyapunov function in some cases, but is not in others. We transform this function thr...

Decomposition of a system into smaller components sometimes allows us to analyze and design the system effectively based on properties of the components. The notion of inputto-state stability (ISS) has been widely used to characterize components that refuse linear-like properties. It is, however, still restrictive, and it cannot cover a lot of saturation mechanisms which often arise in practica...