Decentralized stabilization with controller constraints: |strong and reliable stabilization

Abstract

In this thesis we study two problems in decentralized stabilization. The first is the strong decentralized stabilization problem, which can be stated as follows. Given a plant Z, does there exist a block-dlagonal stable compensator C that internally stabilizes Z? The second is the reliable decentralized stabilization problem. Given a plant Z, does there exist a block-diagonal internally stabilizing compensator C that maintains its stabilizing property in case of interconnection failures in the plant? We show that for two-channel systems the two problems are equivalent in the following sense. The problem of reliabie· decentralized stabilization for a given plant is solvable if and only if the problem of strong decentralized itabilization for another plant (defined explicitly in terms of the original plant) is solvable. Using this main result, we show that: i) For a two-input-two-output plant with all of its zeros stable, the strong decentralized stabilization problem is solvable. ii) For a two-input-two-output plant which has a tansfer matrix with the diagonal elements stable and the off-diagonal elements minimum phase, the reliable decentralized stabilization problem is solvable.