Stability condition of linear time-invariant distributed-order dynamic systems

Bounded-input bounded-output stability condition of linear time invariant (LTI) distributed-order system over integral interval (0, 1) has been established for the first time. Two cases about weighting function of the distributed order are investigated, and sufficient and necessary conditions of stability for these two types of distributed-order systems are derived. Based on the complex integration analysis, timedomain responses of distributed-order systems are also given by analytical method, and numerical examples are presented to illustrate the proposed conditions.