C Appendix: The Discrete DLMI Method

Abstract

We consider the following system:

$$ x_{k+1}=A_kx_k + B_k w_k, \quad k=0,1, \ldots, N-1, \quad z_k = L_k x_k, $$

where $x_k\in \mathcal{R}^n$ is the state vector, $w_k\in\mathcal{R}^q$ is the exogenous disturbance which is assumed to be of finite energy, $z_k\in \mathcal{R}^m$ is the objective vector and x₀ is an unknown initial state.