Stability analysis and control design of LTI discrete-time systems by the direct use of time series data

This paper proposes a new framework for the stability analysis and feedback control design of LTI discrete-time systems, called the data space approach, in which a set of the time series data generated from a system is solely and directly used for control system analysis and design, instead of using a mathematical model such as transfer function, state equation, or kernel representation. In this approach, system dynamics are represented as a subspace of a finite-dimensional vector space, called the data space, whose vectors correspond to all the subsequences of the time series. Furthermore, this data space is supposed to contain all the dynamic behaviors of the system, hence, by using a basis matrix of the data space, we can establish a data-based stability condition based on the Lyapunov stability theory, which enables us to test the stability of an LTI system directly from its time series data. In addition, for feedback controller design, a data-based stabilizability condition is developed by using a geometrical relationship in data spaces. The original intention of this paper is to introduce the basic idea of the data space approach, hence, for its clarity, all the discussions are carried out under the assumptions of noise-free and a priori known system orders, and only the stabilization problem is considered.