Reduced-order Construction of H∞ State Feedback Law for Discrete-time Input-delayed Systems

Abstract

The H ∞ state feedback control problem for discrete-time single input-delay systems is studied based on the min-max optimization and J-spectral factorization theories. The focus is on efficient construction of the H ∞ state feedback law despite the augmented state space due to the input delay. By the min-max optimization approach, the feasibility of the H ∞ disturbance attenuation is characterized in terms of a Riccati difference equation, and the stabilizing solution of the standard KYP equation for the augmented system is constructed from that for the delay-free case. The Jspectral factorization approach is outlined based on the author's previous results. This approach yields another kind of feasibility conditions characterized in terms of a symplectic matrix. The relationship between the first and second approaches is addressed via finite-horizon ℓ 2 -gain analysis.