Generalized integral inequality and application on partial stability analysis

The method of Lyapunov is one of the most effective methods for the analysis of the partial stability of dynamical systems. Different authors develop the problem of partial practical stability based on Lyapunov techniques. In this paper, we investigate the partial practical stability of linear time-invariant perturbed systems based on the integral inequalities of the Gronwall type, in particular of Gamidov's type. We derive some sufficient conditions that guarantee global practical uniform exponential stability with respect to a part of the variables of linear time-invariant perturbed systems. Also, we have developed the local partial practical stability of nonlinear systems. Further, we provide two examples to support our findings.