Chain scattering approach to H infinity control for time-varying systems

The chain scattering approach to the solution of the linear time-invariant (LTI) H infinity control problem proposed in Kimura (1995) is extended to the linear time-varying (LTV) case in this paper. A proof of sufficiency and necessity for (Jmr,Jpr)-lossless and co-(Jmq, Jmr)-lossless factorizations for the solvability of the four-block LTV Hinfinity control problem is shown. The solutions obtained exist in the form of Lyapunov stabilizing solutions to two matrix Riccati differential equations and satisfy a spectral radius coupling condition. A state space proof is also given for the LTVco-(Jmq, Jmr)-lossless embedding theorem in Hinfinity by exploiting the cascade structure of the dual chain scattering formalism and the structural decomposition of the system.