Optimal practical stabilization and controllability of systems with Markovian jumps Original Research Article

Classical Lyapunov theory provides only qualitative type of information from the concept of stability. If one is interested not only in the qualitative behavior but also in the quantitative data, such as specific trajectory bounds and specific transient behavior then practical stability is very useful. In this paper, the practical stabilization is investigated for continuous-time nonlinear systems with Markovian jumps using vector Lyapunov methods. The stabilization is posed in terms of the vector Lyapunov-like function techniques which together with comparison principle allows us to compute the stabilizing controller. Sufficient conditions are established for practical stability criteria in the pth mean under less restrictive conditions compared to the Lyapunov stability for nonlinear systems with Markovian jump perturbations. Finally, controllability and optimal practical stabilization based on the HJB equation are established. Two numerical examples are given to show the fruitfulness of our results.