Control of Linear Discrete-Time Periodic Systems: A Decentralized Control Approach

In this paper, a decentralized control technique is applied to the problem of periodic output feedback stabilization or pole-assignment for a periodically time-varying discrete-time system. It is shown that the problem can be reduced to that of stabilizing or pole-assigning a general proper multi-channel system by static output feedback on the basis of the equivalence between periodic systems and a class of linear time-invariant system. The notion of periodic fixed mode is introduced for a periodic system similar to the notion of uncontrollable or unobservable modes. In terms of this notion, both necessary conditions and sufficient conditions for the solvability of the problem are obained.