Stability and boundedness

Abstract

The general solution of linear time-invariant vibrating systems with given initial conditions and excitation function was determined in Chapter 4. However, in the engineering practice the initial conditions and the excitation function are frequently only approximately known, and because of this the general solution cannot be exactly calculated. Thus the notions of stability and boundedness which describe qualitatively the general behavior of the solution are of fundamental importance for analysing dynamic systems. Stable and bounded systems satisfy the requirement that from small disturbances only small changes in the behavior of the system occur. Such disturbances include here externally applied excitations or deviations in the initial conditions. The theoretical presentation of the stability problem is preceded by the definitions of the concepts of stability and boundedness in Section 5.1. Further, in Section 5.2, the stability of homogeneous systems and their criteria for the verification of stability behavior are investigated. The corresponding treatment of the boundedness problem for inhomogeneous systems follows in Section 5.3.