  In this paper we provide a set of stability conditions for linear
time-varying networked control systems with arbitrary topologies using a
piecewise quadratic switching stabilization approach with multiple quadratic
Lyapunov functions. We use this set of stability conditions to provide a novel
iterative low-complexity algorithm that must be updated and optimized in
discrete time for the design of a sparse observer-controller network, for a
given plant network with an arbitrary topology. We employ distributed observers
by utilizing the output of other subsystems to improve the stability of each
observer. To avoid unbounded growth of controller and observer gains, we impose
bounds on the norms of the gains.
