Dual phase-variable form

1. What is phase variable form?
2. What is observer canonical form?
3. What is controllable canonical form?

What is phase variable form?

Phase variables: The phase variables are defined as those particular state variables which are obtained from one of the system variables & its (n-1) derivatives. Often the variables used is the system output & the remaining state variables are then derivatives of the output.

What is observer canonical form?

The observable canonical form of a system is the dual (transpose) of its controllable canonical form. In this form, the characteristic polynomial of the system appears explicitly in the last column of the A matrix.

What is controllable canonical form?

y = [a0 a1 a2 ··· an−1]x . This form is called the controllable canonical form (for reasons that we will see later). Note how the coefficients of the transfer function show up in the matrix: each of the denominator coefficients shows up negated and in reverse order in the bottom row of A.