Safety Analysis of a Class of Timed Automata Hybrid Systems with SOS

In this paper we investigate safety analysis or reachability of timed automata hybrid systems as an extension of safety analysis of linear systems. The safety verification problem of linear system with certain eigen-structure will be converted to an emptiness problem for semi-algebraic set. Sum of squares (SOS) decomposition will be used to check the emptiness of the set. Suppose given sets of the initial state at mode and terminal set at mode . The safety analysis is solved by determining the solution of the differential solution at mode and the solution of the mode at the discrete occurrence. This solution then becomes the initial condition of the next mode and analysis by using the safety analysis