Numerical Computing Device of Ordinary Differential Equation, Method for Executing Operation Solving Ordinary Differential Equation in Computing Device, Memory Medium Containing Program

A method for executing an operation solving a state equation that is an ordinary differential equation in a computing machine, the ordinary differential equation modeling mathematically an action of an object to be controlled, said method comprising steps of:

• step for setting a state equation, which, with respect to an ordinary differential equation comprising a term of a state variable vector term indicating a state multiplied by a first coefficient matrix and a term of an input vector term indicating an input multiplied by a second coefficient matrix, has a form of a difference equation showing a difference relationship between discrete times determined by a predetermined computing step, in said state equation said first coefficient matrix and said second coefficient matrix each being defined to contain a first matrix power series which approximates a matrix exponential function whose index is a constant matrix that is deemed to be constant invariable during a certain time interval and composed of a power term of a product of a predetermined computing step multiplied by said constant matrix and which is in a finite order;
• step for separating said computing steps into time invariable computing steps invariable in time and time variable computing steps variable in time, and computing, at least, in advance of the operation solving said state equation, a second matrix power series which is composed of a power term of a product of said time invariable computing steps multiplied by said constant matrix and is in said finite order;
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• step for executing the solving operation for said difference equation on the basis of the sequentially computed time variable computing steps, while computing respectively said first coefficient matrix and said second coefficient matrix based on said second matrix power series computed in advance.

A memory storing a program for executing an operation solving a state equation that is an ordinary differential equation in a computing device, the ordinary differential equation modeling mathematically an action of an object to be controlled, the program being for executing the processing steps of:

• processing step for setting a state equation which, with respect to an ordinary differential equation comprising a term of a state variable vector term indicating a state multiplied by a first coefficient matrix and a term of an input vector term indicating an input multiplied by a second coefficient matrix, has a form of a difference equation showing a difference relationship between discrete times determined by a predetermined computing step, in said state equation said first coefficient matrix and said second coefficient matrix each being defined to contain a first matrix power series which approximates a matrix exponential function whose index is a constant matrix that is deemed to be constant invariable during a certain time interval and composed of a power term of a product of a predetermined computing step multiplied by said constant matrix and which is in a finite order;
• processing step for separating said computing steps into time invariable computing steps invariable in time and time variable computing steps variable in time, and computing, at least, in advance of the solving operation for said state equation, a second matrix power series which is in said finite order and composed of a power term of a product of said time invariable computing step multiplied by said constant matrix;
• and
• processing step for executing the solving operation for said difference equation on the basis of the sequentially computed time variable computing steps, while computing respectively said first coefficient matrix and said second coefficient matrix based on said second matrix power series computed in advance.