Discrete control of switched linear systems

Switched linear systems exhibit a continuous state evolving along the continuous flow of time according to linear time invariant differential equations. Furthermore, a discrete interface to the environment is provided, acting on input signals by switching between a finite number of differential equations and generating output signals when the continuous state crosses certain boundaries. We suggest a conservative approximation scheme based on sampling, state partitioning and l-completion realized by a finite past induced state machine. The control problem is investigated on the approximation level. If a solution exists, it also solves the problem for the switched linear system.