The approximate stability for distributed parameter systems

The stability of distributed parameter systems (DPSs) plays an important role in the analysis and synthesis of DPS. But the study of stability of DPSs is more difficult than that of lumped parameter systems (LPSs) due to the distribution characteristics. In this paper, based on the spectrum decomposition theory of partial differential equations, the authors propose some new concepts about the approximate stability of DPSs by means of approximate transformation of orthogonal functions. The definition of the transformation of distributed parameter systems on the basis of orthogonal functions is put forward; and various definitions of approximate stability of DPSs, including approximate stability, asymptotically approximate stability and large range asymptotically approximate stability of DPSs are given; for linear DPSs, the criterion of approximate stability is investigated. Finally, two classes of linear DPSs-first order and second order-are investigated in detail for their approximate stability criteria