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Hybrid analysis of automated manufacturing systems using discrete linear inclusions

Presents a hybrid formulation for the modeling and control of automated manufacturing systems. This approach leads to a linear time-varying discrete-time state variable model which allows fast and direct design of the system configuration. The problem is addressed by splitting the discrete event dynamical process into two hierarchical layers and defining what we call macro-events and macro-states. Then the stability of the system is considered in terms of the stability of discrete linear inclusions, the evolution in time of which is described by language theory and finite automaton methods. We derive structural properties of such a model and we give evidence of an intriguing relationship existing between idempotent matrices and this hybrid formulation of the discrete event processes which drive the dynamic behavior of an automated manufacturing system.