The state vector differential equation

The state of a system is deseribed by a set of first-order differential equations in terms of the state variables (xi, X2,. .., x ) and input variables (u, U2,. .., u ) in the general form 

The equations set (8.1) may be eombined in matrix format. This results in the state veetor differential equation 

Equation (8.2) is generally ealled the state equation(s), where lower-ease boldfaee represents veetors and upper-ease boldfaee represents matriees. Thus 

In general, the outputs (yi,y2, , yn) of a linear system ean be related to the state variables and the input variables 

State-space methods for control system design 235 

---

Discrete-time solution of the state vector differential equation... 

---