A standard linear time-delay system with a single constant delay is typically modeled using the state-space representation:
Robust Control and Filtering for Time-Delay Systems Introduction Robust Control and Filtering for Time-Delay Sys...
ẋ(t)=Ax(t)+Adx(t−h)+Bu(t)x dot open paren t close paren equals cap A x open paren t close paren plus cap A sub d x open paren t minus h close paren plus cap B u open paren t close paren is the state vector. is the delayed state. Adcap A sub d are the system and delay-state matrices, respectively. A standard linear time-delay system with a single
including the initial position of the state at time t = 0. It is required to define a vector function φ : [−h, 0] → R such that x( Archive ouverte HAL (PDF) Robust Control of Time-Delay Systems - ResearchGate including the initial position of the state at time t = 0