Switching Linear Control System Of Linear State Feedback Stabilizability,

A switched system is a hybrid system which consists of a finite number of subsystems and a logical rule that orchestrates switching between these subsystems. Switched systems have recently gained a great deal of attention mainly because many real-world projects such as, mechanical manufacturing, power electronics, systems biology, and Network congestion control can be modelled as switched systems. Dayawansa verified that if there exists a con-troller u(u∈C1) which makes linear control systems exponential stability, then there exists a linear state feedback controller which makes linear control systems exponential stability. Art-stein generalize this conclusion to switched linear control systems. From control theory, we know that if a linear control system is controllable, then a linear state feedback controller exists which makes the system asymptotic stability. In this paper we generalize this conclusion to two dimensional and one kind of special high-dimensional switched linear control systems.