Stability of Positive Fractional 1D and 2D Linear Systems

Asymptotic Stability of Discrete-Time Linear Systems

Positive Discrete-Time Systems

Consider the positive discrete-time linear system:

$$x_{i+1} = Ax_i+Bu_i, \quad\quad(8.1a)$$

$$y_i = Cx_i+Du_i, \quad\quad(8.1b)$$

where $x_i\in{\mathbb R}_+^n, u_i\in{\mathbb R}_+^m, y_i\in{\mathbb R}_+^p$ are the state, input and output vectors and $A\in{\mathbb R}_+^{n\times n}, B\in{\mathbb R}_+^{n\times m}, C\in{\mathbb R}_+^{p\times n}, D\in{\mathbb R}_+^{p\times m}$.