ULTIMATE BOUNDEDNESS CONTROL FOR UNCERTAIN DISCRETE-TIME-SYSTEMS VIA SET-INDUCED LYAPUNOV FUNCTIONS

In this note, linear discrete-time system affected by both parameter a nd input uncertainties are considered. The problem of the synthesis of a feedback control, assuring that the system state is ultimately boun ded within a given compact set containing the origin with an assigned rate of convergence, is investigated. It is shown that the problem has a solution if and only if there exists a certain Lyapunov function wh ich does not belong to a preassigned class of functions (e.g., the qua dratic ones), but it is determined by the target set in which ultimate boundedness is desired. One of the advantages of this approach is tha t we may handle systems with control constraints. No matching assumpti ons are made. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. The resulting compensator may be implemented as a linear variable-structure control.