Why is state-space representation more numerically stable than zeros-poles representation?

1. Why is state space representation important?
2. Why are there more poles than zeros?
3. What is meant by state space representation?
4. What are the poles of a matrix?

Why is state space representation important?

In general, a state space is introduced into a system description without examining its specific physical meaning. It is known, however, that if we select a suitable state space representation, it becomes easier for us to understand or to manipulate the property of a system.

Why are there more poles than zeros?

When a system has more poles than finite zeros (i.e. the transfer function of the system is strictly proper) then the system is causal. If the transfer function of a system has relative degree equal to 0 then the system is causal and there is also instantaneous transfer between input and output.

What is meant by state space representation?

State space representation is a mathematical model of a physical system expressed as a function of input, output, and state variables related by first-order differential equations or difference equations. The state of the system can be represented as a vector within that space.

What are the poles of a matrix?

For state-space models, the poles are the eigenvalues of the A matrix, or the generalized eigenvalues of A – λE in the descriptor case. For SISO transfer functions or zero-pole-gain models, the poles are the denominator roots.