Strong Structural Controllability

For linear time-invariant control systems, the system parameters values may vary or be never known precisely with the exception of fixed zeros determined by the physical structure of the system. Dividing the system parameters into two categories, indeterminate parameters and fixed zero parameters, the notion of strong structural controllability is introduced with the following meaning: A system is strongly structurally controllable if, whatever values (other than zero) the indeterminate parameters of the system may take, the system is controllable.The two necessary and sufficient graph theoretic conditions for linear time-invariant control systems to be strongly structurally controllable are given. The one is fundamental for strong structural controllability and shows what is the essential set of indeterminate parameters the change of whose values may cause a system to be uncontrollable. The other is useful because of its very simple and intuitive form in graph theoretic aspect. For sparse systems, its co...