Probabilistic robust design of LPV control systems

Presents an alternative approach to solve robust performance problems for linear parameter-varying (LPV) control systems. In contrast to previous methods, which are focused on deterministic algorithms, this paper is based on a probabilistic setting. The proposed randomized algorithm provides a sequence of candidate solutions converging with probability one to a feasible solution in a finite number of steps. The main advantages of this method over the previous literature are as follows: (i) the randomized algorithm gives a direct method for general LPV plants with state-space matrices depending on scheduling parameters in a nonlinear manner, i.e. the probabilistic setting does not require any approximation, such as a linear fractional transformation (LFT), of the state space matrices or a gridding on the set of scheduling parameters; (ii) the proposed algorithm is sequential and, at each iteration, it does not require heavy computational effort, such as simultaneously solving a large number of linear matrix inequalities.