General Model

The following type of the state-space model can, in general, describe a continuous­time nonlinear dynamic system:

X — f(x, t, b) + u + w z — h(x, b, K) + v

Here, x is the (nx 1) state vector, u is the (px 1) control input vector, z is the (тех 1) measurement vector, w is a process noise with zero mean and spectral density (matrix), Q, and v is the measurement noise with zero mean and covariance matrix R. The unknown parameters are represented by vectors b and K; x0 is a vector of initial conditions x(t0) at t0. This model is highly suitable for representing many real – life systems, since they are nonlinear. The nonlinear functions f and h are vector­valued relationships and assumed known for the analysis. Several real-life examples of this form will be seen in Chapters 3 and 9.