New Saturated Delayed Control for a Chain of Integrators with Nonlinear Terms

Abstract

This paper investigates the saturated delayed stabilization of a chain of integrators with higher‐order nonlinear terms. With the aid of a recent state transformation, the system is transformed into a canonical form in which time delay appears in both input and states. As a result, natural cancellations can be fully used in the saturation reduction analysis, and fewer terms need to be estimated in the asymptotical stability analysis of the reduced system. In addition, a single tuneable parameter is introduced to the special state transformation, which facilitates compensating an arbitrarily large input‐delay. As an example, a simplified inertia wheel pendulum system is provided with an explicit controller and numerical simulations are given to demonstrate the effectiveness of the suggested controller.

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

“…Consider the Euler discretization of a simplified inertia wheel pendulum (see eq. 26 in the work of Li et al 34 ) with a normalized unitary sampling period, as follows:…”

State space construction for continuous time transfer function matrices via Nerode equivalence

“…The aim of this paper is to show that a simple idea of Nerode's equivalence relation originated in automata theory [2] can be used to deduce a minimal state‐space realization in Jordan canonical form of a rational transfer function matrix in a natural way. It sheds light on the construction of state for general nonlinear purely input–output systems [3], such as time delay systems with dynamic uncertainties; see, e.g., previous studies [4–7]. The minimal state‐space realization of a rational transfer function matrix was first discussed by Gilbert [8] for matrices with simple poles and Kalman [9, 10] for matrices with multiple poles.…”