|# of variables
|# of modes
|# of jumps
|Guards & Invariants
It is a piecewise linear system with different controlled continuous dynamics. The matrices describing the modes of the hybrid system are generated randomly by using the rss() Matlab function. The generated systems are then stabilized with an LQR controller to garantee a convergence to a stable attracting region. The transitions are determined heuristically by means of simulations.
The proposed benchmark consists of 5 modes und 5 transitions. The continuous dynamics in each mode is described by the following ODE:
where is the state vector, is an input signal confined in compact bounded set and
The corresponding hybrid automaton is given in fig.1.
We use the initial set
with the initial location . The time horizion is set to .
SpaceEx results for a time horizon and box directions :