High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the closed-loop systems are constant linear ones with completely assignable eigenstructures. Based on this special feature of the type of HOFA models, controllability of general dynamical control systems is proposed. It is revealed that a general dynamical control system can be represented by a controllable subsystem described by a HOFA model, and an extra uncontrollable one or supplementary one. While a general dynamical control system is called stabilisable if its uncontrollable (autonomous) subsystem does not exist, or is stable in a certain sense. Finally, two parametric design approaches for control of the type of general HOFA models are proposed, which provide all the design degrees of freedom. Several examples, including ones of sub-fully actuated systems, are treated, which demonstrate the effect of the proposed theories.

Automated summary

This paper introduces a new type of high-order fully actuated (HOFA) model for general dynamical control systems, which can be easily designed with controllers. Controllability and stability concepts for general dynamical control systems are discussed based on this model. The paper also proposes two parametric design approaches and provides examples to demonstrate the effectiveness of the theories.