Model reduction of distributed nonstationary LPV systems

$\mathcal{H}_\infty$ Network Optimization for Edge Consensus

“…The usefulness of the proposed optimization paradigm is illustrated via a formation control example with non-homogeneous agents. A potential direction for future research includes designing structure-preserving model reduction techniques, similar to the ones considered in [47,48,49,50], that allow for reducing the system dynamics while re- taining the network interpretation of the reduced-order system.…”

Coprime Factor Model Reduction of Multidimensional Systems

“…, for all 𝛿 ∈ 𝛺, Proof. The proof follows the same line as that of Theorem ( 5) in [7], and Proposition (6) in [5], which are considered for 1-dimensional uncertain systems defined in LFR (Linear Fractional Representation) form. ◻ Remark 2.…”

“…𝑀 is given in (7) are called the parameter-dependent controllability and observability Gramians, respectively, of the system (4) if they satisfy the following matrix inequalities 𝐴(𝛿)𝑋(𝛿)𝐴 * (𝛿) − 𝑋(𝛿 + ) + 𝐵(𝛿)𝐵 * (𝛿) < 0, 𝐴 * (𝛿)𝑌(𝛿 + )𝐴(𝛿) − 𝑌(𝛿) + 𝐶 * (𝛿)𝐶(𝛿) < 0,…”

“…In this case, the balanced truncation technique cannot be applied. Therefore, the system should be stabilized (see Definition 3.3 below), i.e., by constructing a state-feedback controller and defining a stable coprime factor such that the resulting realization is stable, thus, the balanced truncation method can be applied as in [7] for one-dimensional systems and [5] for uncertain systems. This work extends the result of [5] and [7] to the case of parameter-varying multidimensional system which is presented in (4).…”

“…The next theorem is a standard result and it is well-known in many references. So, it is given here without proof since the proof steps are similar to the result in [7,5] for 1dimensional uncertain systems, but here it is applied for parameter-varying multidimensional systems.…”