Unified Invariants for Cyber-Physical Switched System Stability


Cyber-physical systems (CPS) consist of subsystems of distributed computation interconnected by computer networks that monitor and control switched physical entities interconnected by physical infrastructures. Finding a common semantic among these diverse subsystems that facilitates system synthesis, verification, and monitoring is a significant challenge of a CPS research program. Logical and temporal correctness of computational components, network timing, and frequency response are all system aspects that conspire to impede design, verification, and monitoring. Most current approaches ensure that each subsystem meets its individual specifications according to relevant metrics-stability of a physical system, safety and liveness of a cyber system, etc.-and then composes the overall system by functionality. The individual specifications are given in different semantics for each type of subsystem, and are in general equivalent to the cyber notion of correctness. This paper develops common semantics that span each aspect of a CPS through a new approach, unified invariants; unified invariants also ensure individual subsystem correctness but compose the overall system through logical truth instead of functionality. These individual invariants express and enforce system correctness common to the cyber, physical, and networking CPS subsystems and unified invariant approach ensures that the subsystems do not interfere with each others' correctness. In particular, the synthesis of switched dynamic CPSs will be unified by cyber, networking, and physical invariants rooted in the principal of Lyapunov-like functions. The goal is to make the resulting CPSs will be safe and stable at the system level, rather than just the subsystem level.


Electrical and Computer Engineering

Second Department

Computer Science


National Science Foundation (U.S.)
Missouri University of Science and Technology. Intelligent Systems Center
Missouri University of Science and Technology. Energy Research Development Center


This work was supported by the Future Renewable Electric Energy Delivery and Management Center, a National Science Foundation supported Engineering Research Center, under grant NSF EEC-081212; the Missouri S&T Intelligent Systems Center; and the Missouri S&T Energy Research and Development Center.

Keywords and Phrases

Computational Components; CPS; Cyber-Physical Systems (CPS); Distributed Computations; Invariant; Lyapunov-Like; Lyapunov-Like Functions; Temporal Correctness; Embedded Systems; Frequency Response; Specifications; System Stability; Semantics; Stability Analysis; Power System Stability; Switched Systems; Lyapunov Methods; Peer-to-Peer Computing; Switches; Power Engineering Computing

International Standard Serial Number (ISSN)

1949-3053; 1949-3061

Document Type

Article - Journal

Document Version


File Type





© 2014 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2014