Computing whether a system is close to uncontrollable is numerically difficult task. Some preliminary results on a simple experimental approach are presented. The method is based on reducing the problem to a rank problem for a certain matrix pencil. This method exhibits locally quadratic convergence to a local minimum of a function that yields the distance (in the state-space sense) to the nearest uncontrollable system from a given system. The entire computation take place in state space for numerical stability. This algorithm is used to compute the distance for certain examples, and the examples are used to show some severe limitations on the popular staircase algorithm.
|Original language||English (US)|
|Number of pages||4|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - Dec 1 1986|