Restricted control of complex systems with prevention of instability propagation

One of the challenges for complex systems is the issue of limited number of sensors and actuators for controlling relatively abundant number of agents. The infeasibility of large distribution of sensors and actuators prevents many advanced algorithms from exercising their power. Pinning control provides a remarkable resolution to this difficult problem albeit suboptimal solutions are often sought. In this paper, however, a restricted control approach is proposed particularly targeting the problem of controlling complex networks using only one sensor and one actuator at only one node. Performance achievability for both discrete frequencies and over frequency bands are investigated; the important problem of broad band stability is analyzed, and important results are obtained with easy-to-verified conditions; prevention of instability propagation is also delineated using the concept of bounding the controlled agent's norm. Numerical examples are provided for verification of the theoretical results.