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Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

Krumov A. V.

Archives of Control Sciences

2012

Vol. 22, no. 1

43-58

In the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.

On the admissible perturbations for discrete systems

Rachik M., Abdelhak A.

Archives of Control Sciences

2002

Vol. 12, no. 3

301-313

We consider a discrete system described by xi+1=Axi, i>0 with the output function yi=Cxi, i>0 which is subject to the constraints (...). Then we investigate the admissible nonlinear perturbations (Ni)i, i.e., the ones such that the corresponding perturbed output function (...) remains in the constraints set omega for all i>0.