  Periodic control systems used in spacecrafts and automotives are usually
period-driven and can be decomposed into different modes with each mode
representing a system state observed from outside. Such systems may also
involve intensive computing in their modes. Despite the fact that such control
systems are widely used in the above-mentioned safety-critical embedded
domains, there is lack of domain-specific formal modelling languages for such
systems in the relevant industry. To address this problem, we propose a formal
visual modeling framework called mode diagram as a concise and precise way to
specify and analyze such systems. To capture the temporal properties of
periodic control systems, we provide, along with mode diagram, a property
specification language based on interval logic for the description of concrete
temporal requirements the engineers are concerned with. The statistical model
checking technique can then be used to verify the mode diagram models against
desired properties. To demonstrate the viability of our approach, we have
applied our modelling framework to some real life case studies from industry
and helped detect two design defects for some spacecraft control systems.
