Switching Rules for Decentralized Control with Simple Control Laws

We introduce a novel method for enforcing stability on a decentralized control system. In contrast to previous work, our approach allows for the use of a wide variety of simple control laws, while still providing for a formal proof of stability. Our motivating example uses a simple geometric switching function coupled with PD control that has an intuitive interpretation as a virtual spring mesh. Building on this example, we show a general proof technique that applies to a large class of decentralized control systems. Furthermore, we describe additional cases that illustrate how our technique can be applied to useful systems that are straightforward to implement.