Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only

In this paper, the fully actuated system (FAS) approaches for continuous-time systems with time-varying state delays are proposed. Two types of continuous-time high-order FAS models with time delays: single-order time-delay FAS models and multi-order time-delay FASs, are proposed. Particularly, the type of sub-FASs that do not completely but partially satisfy the full actuation is investigated, and the sets of feasible points are defined. When the system states are constrained to the feasible set, a controller can be easily constructed for the sub-FAS such that the closed-loop system is a constant linear system with an arbitrarily assignable eigenstructure. In addition, it is demonstrated that the feasibility constraint can be transformed into a constraint on the initial values of the system, which vanishes when the system is a (global) FAS. Based on the unique control characteristic of the type of FAS models, the concepts of controllability and stabilizability of general dynamical time-delay systems are also proposed. The effect of the proposed theories is illustrated with examples.