Continuous-time and discrete-time positive systems

Abstract

Consider the linear continuous-time system described by the equations

$$ \dot x = Ax + Bu,x(0 = x_0 ) $$

((2.1a))

$$ y = Cx + Du $$

((2.1b))

where $x = x(t) \in R^n$ is the state vector at the instant $t,u = u(t) \in R^m$ is the input vector, $y = y(t) \in R^p$ is the output vector, $A \in R^{nxn} ,B \in R^{nxm} ,C \in R^{pxn} ,D \in R^{pxm} .$