Stability and Control of Dynamical Systems with Applications: A Tribute to Anthony N. Michel, Birkhauser, 2003

Abstract -- In this chapter, a class of discrete time uncertain linear hybrid systems, affected by both parameter variations and exterior disturbances, is considered. The main question is whether there exists a controller such that the closed loop system exhibits desired behavior under dynamic uncertainty and exterior disturbances. The notion of attainability is introduced to refer to the specified behavior that can be forced to the plant by a control mechanism. We give a method for attainability check-ing that employs the predecessor operator and backward reachability analysis, and a procedure for controller design that uses finite automata and linear programming techniques. Finally, Networked Control Systems (NCS) are proposed as a promising application area of the results and tools developed here, and the ultimate bounded-ness control problem for the NCS with uncertain delay, package dropout and quanti-zation effects is formulated as a regulation problem for an uncertain hybrid system.

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