Interval stability/stabilization of impulsive positive systems

This paper investigates the criterion of interval stability of impulsive positive systems with time-varying delay using the idea of generalized pole placement and equivalent systems. Unlike previous stability conditions, the interval stability criterion can more accurately determine the stability of impulsive positive systems. In simple terms, the new criterion can determine the system’s stability and convergence speed. Furthermore, a suitable sufficient condition of interval stabilization is obtained on the basis of the interval stability criterion, which can not only guarantee the stability of impulsive positive systems, but also modulate the state’s convergence rate to the required level. A new algorithm is developed with the interval stabilization approach to accurately control the target system’s convergence rate. Two instances are proposed to prove the superiority of the attainable interval stabilization criterion.