in this paper, a finite-time control scheme is presented for stabilization ofthe satellite chaotic attitude around its equilibrium point whenits attitude is confused by a disturbed torque. controllers and settling timeof stabilizaton are obtained, based on the lyapunov stability theoremand finite-time control scheme. this method is satisfied for any initial condition.numerical simulations are ...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...

A new direct method for the computation of Lyapunov quantities (Lyapunov values or coefficients, Poincare-Lyapunov constants, focus values) for the second-order dynamical system, permitting us to narrow the requirements on a smoothness of system, is obtained.

In this paper, we propose a Lyapunov function design method using a difference approximation scheme and quantization of the Markov process. First, we approximate a Lyapunov equation by a Schrödinger-like equation. Second, we obtain sufficient conditions for a function to be a Lyapunov function. Then, we provide a Lyapunov function design procedure.

In this paper we propose a numerical method for computing all Lyapunov coefficients of a discrete time dynamical system by spatial integration. The method extends an approach of Aston and Dellnitz (1999) who use a box approximation of an underlying ergodic measure and compute the first Lyapunov exponent from a spatial average of the norms of the Jacobian for the iterated map. In the hybrid meth...

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapuno...

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...