Stability Analysis of Discrete Event Control Systems Based on Connection Matrices and Graphs

There are many finite-state and event-driven types of discrete systems, e.g., manufacturing processes, industry and welfare robots, and networked control systems, and so on. However, the analysis and design of such discrete control systems have not been established, because those systems have severe nonlinear characteristics and do not respond continuously in time. In this paper, the stability of discrete event control systems is studied based on multiple metrics and simultaneous inequalities. Especially, in this paper, the structures of discrete event types of systems are analyzed using connection matrices (i.e., permutation (0,1)-matrices). The relationship between connection matrices and graph representations is also reviewed in general. A stability condition is derived based on the concept of nonnegative inverse matrices (so-called M-matrices). Numerical examples were shown to clarify the stability and boundedness of discrete-event control systems.