Stability Analysis of Time Delay Switched Positive Systems with Partially Unstable Subsystems

This technical document investigates the stability problem of switched positive systems (SPSs) with time delays and partially unstable subsystems. Firstly, the presence of partially unstable subsystems and the possibility of unbounded time delays are considered. Under specific conditions, a series of functions are constructed. These functions are positive, monotonically decreasing, and converge to zero as time approaches infinity. Secondly, by employing this novel approach, stability conditions for SPSs with time delays and partially unstable subsystems are established. The results show that these functions can serve as an upper bound for the system trajectories starting from a particular region. Finally, a numerical example is presented to demonstrate the effectiveness of the derived results.