  This article presents a new technique for suboptimal consensus protocol
design for a class of multiagent systems. The technique is based upon the
extension of newly developed sufficient conditions for suboptimal
linear-quadratic optimal control design, which are derived in this paper by an
explication of a noniterative solution technique of the infinite-horizon linear
quadratic regulation problem in the Krotov framework. For suboptimal consensus
protocol design, the structural requirements on the overall feedback gain
matrix, which are inherently imposed by agents dynamics and their interaction
topology, are recast on a specific matrix introduced in a suitably formulated
convex optimization problem. As a result, preassigning the identical feedback
gain matrices to a network of homogeneous agents, which acts on the relative
state variables with respect to their neighbors is not required. The
suboptimality of the computed control laws is quantified by implicitly deriving
an upper bound on the cost in terms of the solution of a convex optimization
problem and initial conditions instead of specifying it a priori. Numerical
examples are provided to demonstrate the implementation of proposed approaches
and their comparison with existing methods in the literature.
