A probabilistic approach to robust control

Considers a probabilistic approach to robust control. We construct explicitly the probability density function for the associated distribution of a random sample set of the robust performance index function which itself is a function of a vector of random variables. Using this probability density function, we derive several bounds on the minimum sample size required to estimate a robust performance index function with prescribed probability and confidence. These bounds show that the probabilistic approach to the robust control analysis and synthesis based on this framework has low complexity. Furthermore, a way of constructing the distribution function of the performance index function is proposed which gives the tradeoff between the performance and the risk