A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

Abstract

This paper suggests a novel nonlinear state feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov-Krasovskii stability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coefficients of the nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to find the proper feedback gain matrix F is also provided. The robustness purpose against nonlinear functions and time-delays is guaranteed in this scheme. Moreover, the problem of robust H ∞ performance analysis for a class of nonlinear time-delayed systems with external disturbance is studied in this paper. Simulations are presented to demonstrate the proficiency of the offered technique. For this purpose, an unstable nonlinear numerical system and a rotary inverted pendulum system have been studied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendulum is provided. These results confirm the expected satisfactory performance of the suggested method.

Output tracking control with preview action for a class of continuous-time Lipschitz nonlinear systems and its applications

“…In Rehan et al (2011), both stabilization and tracking problems of a class of more general Lipschitz systems were discussed via a nonlinear state feedback controller and the existence condition for such a controller was established in terms of linear matrix inequalities. This research routine was later extended to switched systems (Niu and Zhao, 2013) and time-delay systems (Mobayen and Pujol-Vázquez, 2018) with Lipschitz nonlinearities. In addition, some new developments in aspects of consensus control (Ding, 2014), synchronization, (Mobayen and Tchier, 2018) and sliding mode control (Mobayen and Tchier, 2016; Mobayen and Tchier, 2018) have been made for Lipschitz nonlinear systems.…”

Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

“…Indeed, the inequality (35) provided in Theorem 11 cannot be applied directly due to the presence of some uncertain terms. Thanks to Lemmas 8 and 9, the condition in…”

“…It should be emphasized that our proposed controller design is developed via the error system method; therefore, this method which is used to study stability problem is quite different from that in [32][33][34]. In addition, it should be mentioned that the controller design schemes discussed in [18,35] are only effective for achieving stabilization of Lipschitz systems and not suitable to deal with the tracking problem considered here.…”

“…System(33) with ( ) = 0 is first considered. We implement a congruence transformation to(35) with an invertible symmetric matrix Γ defined by…”

Research on secure control and communication for cyber-physical systems under cyber-attacks

“…The essence of fault tolerance and attack tolerance is to solve the system security problem. Inspired by Nakahira and Mo (2018) and Mobayen and Pujol-Vázquez (2017), this paper adopts active fault-tolerant control for faults and passive attack-tolerant strategy against cyber-attacks, which satisfy the robust H ∞ performance of fault tolerance and attack tolerance. The main work is to design the observer firstly to estimate the state and faults online and be robust to the attacks.…”