Abstract
This paper considers robust control analysis and synthesis problems via the expression of our previously proposed summational type state equation. The summational type state equation is a mathematical expression to solve two essential problems, i.e., one of them is a physical problem of discontinuity in mathematical expressions e.g. the controllable canonical form for different orders of the existing state equation, and the other one is an engineering problem of disunification in which continuous-time and discrete-time systems are not described with consistency. First, this paper introduces the summational type state equation. Next, a robust stability analysis condition and a feasible condition for the scaled H∞ control synthesis problem are derived from the summational type state equation. Furthermore, the relation between analysis/synthesis conditions based on summational and difference type state equations is clarified. Finally, the effectiveness of the summational type state equation is shown by numerical examples on a sensitivity minimization problem. From these results, this paper points out that the summational type state equation is one of possible important mathematical expressions in control theory.
