Stability analysis of multirate sampled-data control systems

The paper considers the stability of finite-dimensional linearmultirate sampled-data control systems. A notion of internalstability is defined, based on continous-time singals. A completeproof is given for the equivalence between continuous-time internalstability and discrete-time internal stability. An input-outputproperty called L^v(1v ) hybrid stability is investigated formulatirate systems having exogenous continuous-time inputs andoutput, and hybrid stability is shown to be equivalent to internalstability, which is fundamental to a true development of multiratesampled-data L^v control design. The relationship between internalstability and input-output stability is also discussed in continuoustime.