Decentralized Blocking Zeros-Part II: A Unifying Approach to Decentralized Synthesis Problems

Three main large scale system synthesis problems are considered: (p1) Stabilization of interconnected systems using locally stabilizing subsystem controllers, (p2) Stabilization of a multi-channel system via stabilization of its main diagonal subsystems, and (p3) Reliable decentralized stabilization problem. It turns out that all three problems are special cases of a unifying problem of decentralized simultaneous stabilization, called the decentralized concurrent stabilization problem (DCSP). We obtain a solution to DCSP by formulating it as a decentralized strong stabilization problem on an appropriate auxiliary plant. Specialization of the main result on DCSP to problems (p1)-(p3) yields that (p1)-(p3) are solvable if and only if the set of poles and the set of unstable decentralized blocking zeros of an auxiliary plant satisfy a parity interlacing property.