Summary The optimal linear‐quadratic‐Gaussian synthesis design approach and the associated separation principle are investigated for the case where the observer design model is a reduced model of the underlying system model. Performance of the resulting reduced‐order controller in the full‐state system environment is formulated in terms of an augmented state vector consisting of the system state vector and the reduced model state vector. Considering explicitly separated linear control and estimation laws, a calculus of variations/Hamiltonian approach is used to determine the necessary conditions for the optimal controller and observer gains for the simplified algorithms. Results show that the optimal gains are not separable, ie, the optimal controller and observer gains are coupled and cannot be computed independently. Numerical examples of an infinite‐horizon and finite‐horizon control and estimation large‐scale multiagent system problem clearly show the advantages of using the nonseparable coupled solutions.

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Orthogonal projection-based reduced order models (PROM) are the output of widely-used model reduction methods. In this work, a novel product form is derived for the reduction error system of these reduced models, and it is shown that any such PROM can be obtained from a sequence of 1-dimensional projection reductions. Investigating the error system product form, we then define interface-invariant PROMs, model order reductions with projection-invariant input and output matrices, and it is shown that for such PROMs the error product systems are strictly proper. Furthermore, exploiting this structure, an analytic H∞ reduction error bound is obtained and an H∞ bound optimization problem is defined. Interface-invariant reduced models are natural to graph-based model reduction of multi-agent systems where subsets of agents function as the input and output of the system. In the second part of this study, graph contractions are used as a constructive solution approach to the H∞ bound optimization problem for multi-agent systems. Edgebased contractions are then utilized in a greedy-edge reduction algorithm and are demonstrated for the model reduction of a first-order Laplacian controlled consensus protocol.