Steady-state optimal control for continuous-time systems with input delays

This paper revisits the linear steady-state quadratic optimal control problem for continuous-time systems with multiple input delays. Our aim is to give an intuitive and simple solutions to such problems by adopting the reorganized innovation analysis approach. The design of the optimal controller involves in solving one Diophantine equation and one spectral factorization with time-delays, which is the key to be solved. It will be shown that spectral factor can be obtained by solving standard Riccati equations with the same dimension as the original systems.