Global stabilization of linear systems subject to input saturation and time delays

Abstract This note is concerned with global stabilization of linear systems subject to input saturation and time delays. Based on the Luenberger canonical form, two new decoupling methods are proposed. For the decoupled system, according to some special canonical forms, we propose two control laws for systems with input time-delays and systems with input saturation and time-delays, and give explicit conditions to ensure the global stability of the closed-loop system. Two special canonical forms contain time delays in input and state vectors, which is essential in recursive design. In addition, for the system subject to input saturation and time-delay, we introduce some free parameters when designing the controller, which can improve the instantaneous performance of the closed-loop system. Finally, the proposed approach is applied on the multi-agent system to design global stabilizing controllers and the effectiveness of the proposed controllers are illustrated by numerical simulations.

[1]  F. Gouaisbaut,et al.  Overview of recent advances in stability of linear systems with time‐varying delays , 2019, IET Control Theory & Applications.

[2]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

[3]  Sabine Mondié,et al.  Global asymptotic stabilization for chains of integrators with a delay in the input , 2003, IEEE Trans. Autom. Control..

[4]  Guang-Ren Duan,et al.  Truncated predictor feedback for linear systems with long time-varying input delays , 2012, Autom..

[5]  Bin Zhou,et al.  Global Stabilization of the Multiple Integrators System by Delayed and Bounded Controls , 2016, IEEE Transactions on Automatic Control.

[6]  O. J. M. Smith,et al.  A controller to overcome dead time , 1959 .

[7]  Yacine Chitour,et al.  Linear Systems Subject to Input Saturation and Time Delay: Global Asymptotic Stabilization , 2007, IEEE Transactions on Automatic Control.

[8]  Bin Zhou,et al.  Global stabilization of feedforward nonlinear time-delay systems by bounded controls , 2018, Autom..

[9]  M. Krstić.  Compensation of Infinite-Dimensional Actuator and Sensor Dynamics , 2010, IEEE Control Systems.

[10]  I. Jordanov,et al.  Numerical modeling of dynamics of a population system with time delay , 2017, 1701.08130.

[11]  D. Luenberger.  Canonical forms for linear multivariable systems , 1967, IEEE Transactions on Automatic Control.

[12]  Bin Zhou,et al.  Input delay compensation of linear systems with both state and input delays by adding integrators , 2015, Syst. Control. Lett..

[13]  Zongli Lin,et al.  Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach , 2010 .

[14]  Yonggang Chen,et al.  Robust Stabilization for Uncertain Saturated Time-Delay Systems: A Distributed-Delay-Dependent Polytopic Approach , 2017, IEEE Transactions on Automatic Control.

[15]  Zongli Lin,et al.  A further result on global stabilization of oscillators with bounded delayed input , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Qing-Long Han,et al.  Networked control systems: a survey of trends and techniques , 2020, IEEE/CAA Journal of Automatica Sinica.

[17]  Li Sun,et al.  Control of a Class of Industrial Processes With Time Delay Based on a Modified Uncertainty and Disturbance Estimator , 2016, IEEE Transactions on Industrial Electronics.

[18]  Xinghuo Yu,et al.  Sliding Mode Control With Mixed Current and Delayed States for Offshore Steel Jacket Platforms , 2014, IEEE Transactions on Control Systems Technology.

[19]  Bin Zhou,et al.  Stabilization of Discrete-Time Systems With Multiple Actuator Delays and Saturations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Shengyuan Xu,et al.  Quantized feedback stabilization of continuous time-delay systems subject to actuator saturation , 2018, Nonlinear Analysis: Hybrid Systems.

[21]  Yuanqing Xia,et al.  Adaptive Control for Teleoperation System With Varying Time Delays and Input Saturation Constraints , 2016, IEEE Transactions on Industrial Electronics.

[22]  Maurício C. de Oliveira,et al.  Stability independent of delay using rational functions , 2009, Autom..

[23]  Long Wang,et al.  Finite-time information consensus for multi-agent systems with fixed and switching topologies , 2009 .

[24]  Yong He,et al.  Stability analysis of systems with time-varying delay via relaxed integral inequalities , 2016, Syst. Control. Lett..

[25]  Shengyuan Xu,et al.  Relaxed conditions for stability of time-varying delay systems , 2017, Autom..

[26]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .