Control of uncertain systems represented by linear constraints: maintainability

Considers the control of systems whose dynamics are described by linear constraints. Such dynamics can be expressed in the form of slack-descriptor models. Under the uncertain dynamics of the system, the next-state estimate of the system is a set of possible states. We consider the problem of tube maintainability: determining if there exist controls that will ensure that the set of next possible states will lie within a given tube (a prespecified region of the state space) for any current state in the tube. It is shown that, while in general, the set of all maintaining controls can be approximately described through linear constraints, in some cases this description can be made exact. A method has been presented to derive these linear constraints