Approximate bisimulations for constrained discrete-time linear systems (ICCAS 2015)

In this paper, we consider the problem of approximate bisimulations for constrained discrete-time linear systems. First, we develop a theory of approximation for transition systems with nondeterministic evolution. Then observation metrics are used to describe the bounded distance between system observations. Furthermore, we utilize a class of Lyapunov-like functions, called bisimulation functions, to characterize the approximate bisimulation relations. For the class of discrete-time linear systems with constrained inputs, we convert the problem of computing bisimulation functions to linear matrix inequalities (LMIs) and optimization problems. Finally, a numerical example is performed to verify the effectiveness of the approximation bisimulation framework design technique, and using multi-parametric toolbox (MPT), we also demonstrate the application to safety verification.