This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called the dynamical structure function, characterizes the signal structure , or open-loop causal dependencies among manifest variables, capturing a significantly richer notion of structure than the sparsity pattern of the transfer function. The design technique sequentially constructs each link in an arbitrary controller signal structure, and the main result proves that the resulting controller is either stabilizing or no controller with the desired structure can stabilize the system.
Abstract: This paper studies the effect of decentralized feedback on the closed-loop properties of jointly controllable, jointly observablek-channel linear systems. Channel interactions within such systems are described by means of suitably defined directed graphs. The concept of a complete system is introduced. Complete systems prove to be precisely those systems which can be made both controllable and observable through a single channel by applying nondynamic decentralized feedback to all channels. Explicit conditions are derived for determining when the closed-loop spectrum of ak-channel linear system can be freely assigned or stabilized with decentralized control. This paper considers designs of decentralized controllers for continuous-time linear time-invariant multivariable control systems. The purpose is to show how to attain robust stability and robust performance of decentralized control systems by sequential design procedure. Compared with independent designs in which each controller block is designed independently of others, sequential designs can reduce conservatism associated with the controller design since they can exploit information about the other loops which have been already designed. A novel method of sequential designs for the robust performance are proposed. Moreover, an approach to a kind of failure tolerance is considered. The proposed sequential design procedure is based on expanding construction of decentralized control systems, so that the proposed methods can deal with extension of subsystems.