Quantitative Analysis of Jump Markovian Nonlinear Stochastic Hybrid Systems: Practical Stability

Abstract

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 concept of practical stability is investigated for continuous-time nonlinear stochastic systems of Ito-Doob type with Markovian jumps. Using the practical stability results one can study the qualitative behaviour of the system as well as the quantitative data, such as the specific trajectory bounds and transient behavior of the system. The concept of comparison principle based on vector Lyapunov-like functions are utilized to develop, sufficient conditions for various types of practical stability criteria in the p-th mean of the solution processes of the system under the Markovian jump perturbations. A numerical example is given to show the fruitfulness of our results.