Input-output stability of sampled-data systems

The authors study the L_p input-output stability of a continuous-time controller, using the usual arrangement of periodic sampling and zero-order hold. It is noted that even if the hybrid system is exponentially stable, this arrangement does not yield L_p (1⩽p<∞) stability in general. It is shown that this problem can be alleviated if a strictly causal stable continuous-time filter (e.g. antialiasing filter) is introduced prior to the sampler. For various configurations, L _p stability is examined in connection with exponential stability