Block diagram of state space model

1. What is meant by state space model?
2. How do you represent a state space?

What is meant by state space model?

Definition of State-Space Models

State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations.

How do you represent a state space?

The state space representation is to represent a system in the form of x(k + 1) = f (x(k), u(k), k) and y(k) = g(x(k), u(k), k). If the system is linear, then four time varying matrices A(k), B(k), C(k) and D(k) exist, such that x(k + 1) = A(k)x(k) + B(k)u(k) and y(k) = C(k)x(k) + D(k)u(k).