Data-based Stability Analysis for Linear Time-invariant Discrete-time System
Un Sik PARK, Masao IKEDA
This paper proposes a new framework of stability analysis for linear time-invariant discrete-time systems based on experimental input and output data, in which no mathematical model such as a state equation or transfer function is employed unlike conventional model-based stability analyses. In this framework, we first develop a data-based stability condition for open-loop systems by using a set of output data of a zero-input response, which constitutes a basis of the entire output data space. Then, we consider an output feedback control law and present a data-based stability condition for closed-loop systems by using a set of input and output data of the controlled system, whose linear combinations span the entire closed-loop data space. Both of these data-based stability conditions are derived by the Lyapunov's second method and enable us to investigate stability of dynamical systems directly from the behaviors, i.e., the input and output data.