THEORY OF NONLINEAR FEEDBACK UNDER UNCERTAINTY

Our main purpose here is to demonstrate the potential of a new approac h which is an important expansion of the feedback concept: we have cho sen what seemed a natural way of tackling some traditional problems of the control theory and of comparing the results against those offered by conventional methods. The main problem considered is the output st abilization for uncertain plants. Using structural transformations, un certain systems can change to the form convenient for output feedback design. Synthesis of observer-based control for asymptotical stabiliza tion or uniform ultimate boundedness of the closed-loop system is prov ided. We consider the notions of asymptotic and exponential invariance of a control system implies its suboptimality. A method is described for stabilization of uncertain discrete-time plants of which only comp act sets are known to which plants parameters and exogenous signals be long. New approaches for solving some central problems of mathematical control theory are considered for nonlinear dynamical systems. New cr iterious of local and global controllability and stabilizability are i ndicated and some synthesis procedures are suggested.