J-lossless factorization and H-infinity control for discrete-time systems

摘要

(J,J')-lossless factorization and the chain-scattering representation of the plant have been proposed as a theoretical framework of H-infinity control for continuous-time systems. Recently, these notions were extended to discrete-time systems. The extensions were by no means straightforward, and they clarified the essential differences between continuous-time and discrete-time cases. In this paper, discrete-time H-infinity control problem is solved based on the extension of (J, J')-lossless factorization to discrete-time systems. A necessary and sufficient condition for the solvability of H-infinity control problem is obtained. The condition is represented in terms of two Riccati solutions as in continuous-time cases, but their structures are much more complicated than in continuous-time cases. The results are not new, systematic, self-contained and most general, but the derivation is completely new, demonstrating an intrinsic characteristic feature of discrete-time H-infinity control which has not been exposed by the existing methods based on the direct analogies to continuous-time systems including bilinear transformation. [References: 19]