Multi-rate control system design for distributed parameter systems via induced L2 mixed sensitivity optimization

The problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under multi-rate sampled-data control is discussed in this paper. A weighted H^∞-style mixed-sensitivity measure penalizing the control is used to define the concept of optimality. Controllers are found by solving a finite-dimensional sampled-data optimization. A priori computable conditions for the approximants are provided such that the resulting finite-dimensional controllers stabilize the multi-rate sampled-data controlled distributed parameter plant and are near optimal. The proof is dependent upon a key fact that the control input is appropriately penalized in the optimization. Another assumption of the presented technique is the plant may be approximated uniformly by finite-dimensional systems. It is shown how the optimal performance may be approximated to any desirable level accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. No finite-dimensional spectral factorizations have been utilized. This paper provides a straight forward approach of control design for a large class of MIMO distributed parameter systems under multi-rate sampled-data control.