1. Getting Started

1.1 Using the Application for the First Time

<< ControlSystems`

1.3 The Control Objects

TransferFunction[s, (1/s)]

StateSpace[%]

ToDiscreteTime[TransferFunction[s, (1/s)], 
      Sampled -> Period[T]]

ToContinuousTime[%]

1.4 Traditional Notations

(system  =  
          TransferFunction[s,  {{(1/s)}, {(1/(s + α))}}]) // 
      TraditionalForm

ToDiscreteTime[%, Sampled -> Period[2]] // Simplify // 
      TraditionalForm

StateSpace[system] // TraditionalForm

% // EquationForm

ToDiscreteTime[%,  Sampled ->  Period[τ]] // Simplify // 
      EquationForm

% // TraditionalForm

%

1.5 The Control Format

Table[i + j, {i, 2}, {j, 3}]

StateSpace[{{0}}, {{1}}, {{1}}]

1.6 The Notation for the Imaginary Unit

(
Unprotect[
        Complex]; 
Format[Complex[x_, y_]] := 
        x + "\[ImaginaryJ]" y; 
Protect[
        Complex];
)

2 + 3 (Sqrt[-1])

1.7 Numericalizing for Speed

Array[Random[Integer] &, {4, 4}]

Eigenvalues[%] // Timing

Eigenvalues[N[%%]] // Timing