MIMO, x, w Unobserved, w ≠ 0 Exogenously Generated

Abstract

Consider system

$$\displaystyle\begin{array}{lll}{ x}^{+}& =& Ax + Bu + Ew \\ y& =& Cx \\ e& =& y - y_{d} \\ \end{array}$$

where x ∈ ℝ ⁿ is non-accessible to measurement, u ∈ ℝ ^m, w ∈ ℝ ^q, y ∈ ℝ ^p. We still assume m, p ≤ n, rank C = p, rank B = m and w is a disturbance generated by the exo-system

$$\displaystyle\begin{array}{lll}{ w}^{+}& =& Sw \\ y_{d}& =& Dw \\ \end{array}$$

with S antistable. The control task is to ensure convergence to zero of the error for whatever initial condition x ₀, w ₀.