Practical Exponential Stability and Applications of Switched Impulsive Homogeneous Positive Nonlinear Systems With Stable and Unstable Subsystems

This paper studies the practical exponential stability of switched impulsive homogeneous positive nonlinear systems composed of both stable and unstable subsystems, including continuous‐time and discrete‐time systems. Specifically, we introduce a class of nonnegative impulses that are consistent with the switching behavior of the systems. It should be emphasized that a special switching sequence and switching‐impulsive signals are designed for the systems. First, by using the max‐separable Lyapunov function method and introducing an impulse strength parameter, we establish several new sufficient stability criteria. Second, we derive a new relation between the average dwell‐time parameter and the impulse strength parameter, and analyze the case of different impulse strength parameters. Then, based on the comparison principle, we apply the obtained stability criteria to time‐varying switched impulsive homogeneous nonlinear systems, which are not restricted to being positive, and this holds for both the main systems and the subsystems. Finally, four examples and a specific algorithm verification procedure are provided to illustrate the effectiveness of the obtained results.