A systematic approach is proposed for determining the probability of instability for a controlled structure with real parameter uncertainty. Both an eigenvalue criterion and the RouthHurwitz criterion are employed in the problem formulation to characterize the stability of the system. The uncertain parameters are modeled as random variables with prescribed probability distributions. First and second order reliability methods (FORM/SORM) are discussed and shown to be appropriate for calculating the probability of system instability. Several examples are provided to illustrate the approach.
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