Discrete-time solution of the state vector differential equation

3 Discrete-time solution of the state vector differential equation 

The discrete-time solution of the state equation may be considered to be the vector equivalent of the scalar difference equation method developed from a z-transform approach in Chapter 7. 

State-space methods for control system design 245 

The continuous-time solution of the state equation is given in equation (8.47). If the time interval t — to) in this equation is T, the sampling time of a discrete-time system, then the discrete-time solution of the state equation can be written as 

Equation (8.76) is called the matrix vector difference equation and can be used for the recursive discrete-time simulation of multivariable systems. 

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