On the L₂-Stability of Linear Systems with Time-Varying Parameters

Abstract

In linear control systems, system parameters often vary as functions of time under the influence of environmental conditions; such systems are called as time-varying parameter systems. Methods of analysis depend on the type of available information on the time-varying parameters. In this paper, upper bounds of the time-varying parameters are assumed to be known deterministically. Using functional analysis, stability theory of the linear systems in L₂-space is discussed in relation to the frequency response of the undisturbed original system. Sufficient condition of stability is obtained for the generalized linear system. Also stability of the systems of which open loop characteristics are expressed as Zadeh's system function is briefly discussed. Finally some illustrative examples are presented.