Viewing hybrid systems as products of control systems and automata

Shows how hybrid systems can be modeled as products of nonlinear control systems and finite state automata. A hybrid system is a network consisting of a continuous, nonlinear control system connected to a discrete finite-state automation. The point of view taken is that the automation switches between the control systems, and that this switching is a function of the discrete input symbols or letters that it receives. It is shown how a nonlinear control system can be viewed as a pair consisting of a bialgebra of operators coding the dynamics, and an algebra of observations coding the state space. It is also shown that a finite automation has a similar representation. A hybrid system is then modeled by taking suitable products of the bialgebras coding the dynamics and the observation algebras coding the state spaces