Safety Analysis of Timed Automata Hybrid Systems with SOS for Complex Eigenvalues - Megawati, Noorma Yulia (2011)
In this paper we investigate a safety analysis or reachability of timed automata hybrid systems as an extension of safety analysis of linear systems. The safety verification problem of linear systems with complex eigenvalues will be converted to an emptiness problem from semi algebraic set. Sum of square (SOS) decomposition will be used to check the emptiness of the set. Suppose given set of initial state of mode i and final state at mode i+1. The safety analysis is solved by determining the solution of differential systems at mode i and the solution of mode i at the time occurrence. The solution then become initial state at mode i+1 and then we analyze by using safety analysis of linear systems.