Necessary and sufficient conditions for robust reliable control in the presence of model uncertainties and system component failures

This paper provides necessary and sufficient conditions for several forms of controlled system reliability. For comparison purposes, past results on the reliability analysis of controlled systems are reviewed and several of the past results are shown to be either conservative or have exponential complexity. For systems with real and complex uncertainties, conditions for robust reliable stability and performance are formulated in terms of the structured singular values of certain transfer functions. The conditions are necessary and sufficient for the controller to stabilize the closed-loop system while retaining a desirable level of the closed-loop performance in the presence of actuator/sensor faults or failures, as well as plant-model mismatches. The resulting conditions based on the structured singular value are applied to the decentralized control for a high-purity distillation column and singular value decomposition-based optimal control for a parallel reactor with combined precooling. Tight polynomial-time bounds for the conditions can be evaluated by using available off-the-shelf software.

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