Stability analysis of multirate sampled-data control systems

The paper considers the stability of finite-dimensional linear multirate sampled-data control systems. A notion of internal stability is defined, based on continous-time singals. A complete proof is given for the equivalence between continuous-time internal stability and discrete-time internal stability. An input-output property called L^v(1≦v≦ ∞) hybrid stability is investigated for mulatirate systems having exogenous continuous-time inputs and output, and hybrid stability is shown to be equivalent to internal stability, which is fundamental to a true development of multirate sampled-data L^v control design. The relationship between internal stability and input-output stability is also discussed in continuous time.