Statespacemuodot
Statespacemuodot refer to a family of mathematical representations used to model dynamic systems by encapsulating the system’s internal state and its evolution over time. A state-space model describes the system with a state vector x(t) (or x_k in discrete time) and an output vector y(t) that depends on the state and input u(t). In continuous time, the evolution is given by x'(t) = f(x(t), u(t), t) and y(t) = g(x(t), u(t), t). In linear time-invariant form, these become x' = Ax + Bu and y = Cx + Du. In discrete time, the standard form is x_{k+1} = Φ x_k + Γ u_k and y_k = H x_k + D u_k.
The state vector is interpreted as a minimal sufficient statistic for predicting future behavior under a given
Extensions commonly include stochastic components: x_{k+1} = Ax_k + Bu_k + w_k and y_k = Cx_k + Du_k + v_k, where w_k
Applications span control engineering, robotics, aerospace, economics, and biological systems. State-space forms are contrasted with transfer-function