抄録
A primal-dual setting is presented for probabilistic feasibility of a robust Linear Matrix Inequality (LMI), where the coefficients of the LMI depend on uncertain parameters. The primal problem is to find decision variables satisfying the robust LMI for almost all uncertain parameter values, where a probability measure is introduced onto the uncertainty set. Then, a probabilistic dual formulation is introduced as a system of an integral inequality and integral equations. It is proved that the probabilistic primal problem is infeasible if and only if the probabilistic dual problem is feasible. As an application of this result, a standard LMI feasibility problem is also tackled.
