2006 Volume 19 Issue 4 Pages 132-141
This paper proposes a useful expression of summational type state equation conformable to physical and/or engineering actualities. The summational type state equation can solve the following two essential problems in mathematical expressions of the existing state equations : One of them is a physical problem of discontinuity in mathematical expressions for different orders of the existing state equation related to the number of inevitable many parasitic energy elements which always exist in an actual system. The other one is an engineering problem of disunification in mathematical expressions in which continuous-time and discrete-time systems are not described with consistency. First, this paper clarifies and explains the above problems to be solved with a simple example. Next, this paper defines the summational type state equation for the problems and analyzes, for example, basic properties, stability condition and Lyapunov inequality by using the defined state equation. Finally, the effectiveness of the summational type state equation is shown by numerical examples on the stability analysis. From these results, this paper points out that the proposed state equation can overcome difficulties of the above problems and get benefits from the sophisticated results of modern control theory.