Chapter 9.6, Problem 2E

Interpretation Introduction

Interpretation:

• a) To show that the error dynamics are

  $\begin{array}{l}{\text{e}}_{\text{1}}\equiv 0\\ {\dot{\text{e}}}_{\text{2}}=-{\text{e}}_{\text{2}}-{\text{x(t)e}}_{\text{3}}\\ {\dot{\text{e}}}_{\text{3}}={\text{x(t)e}}_{\text{2}}-{\text{be}}_{\text{3}}\end{array}$

• b) To show ${\text{V = e}}_{\text{2}}^{\text{2}}{\text{ + e}}_{\text{3}}^{\text{2}}$ is a Liapunov function

• c) To give the conclusion from the above results.

Concept Introduction:

• ➢ The main idea behind the sending the secret message using chaos is while transmitting the message it is masked by louder chaos. The eavesdropping person only hears only chaos, but the receiver perfectly reproduces chaos and subtracts it from the masked message and hears the original message sent by the transmitter.

• ➢ The error dynamics is calculated by

  $\begin{array}{l}{\text{e}}_{\text{1}}=\text{x}-\text{x(t)}\\ {\text{e}}_2\text{= y}-{\text{y}}_{\text{r}}\\ {\text{e}}_{\text{3}}=\text{z}-{\text{z}}_{\text{r}}\\ {\dot{\text{e}}}_{\text{2}}=\dot{\text{y}}-{\dot{\text{y}}}_{\text{r}},\\ {\dot{\text{e}}}_{\text{3}}=\dot{\text{z}}-{\dot{\text{z}}}_{\text{r}},\end{array}$