Positive effects of time delays on the stability of switched control systems with partial state feedback information

In this paper, a novel state-dependent switching controller with delayed positive partial state feedback is proposed to stabilise a controlled system with insufficient state information. At first, the controlled system is converted to a single-degree-of-freedom vibrational system by using an invertible transform and a second-order Taylor approximation for the time delay term. Then, appropriate control gain parameters and a state-dependent switching rule are designed via the physical meaning of the resulting vibrational system. By combining the advantages of delayed positive position feedback with the state-dependent switching mechanism, we find that the time delay can considerably improve the asymptotic stability of the controlled system. Finally, three numerical examples show that the proposed controller is effective and that time delay indeed plays a prominent positive role in switched control systems.

[1]  Yusheng Zhou,et al.  Stabilization of switched time-delay systems with only unstable subsystems: a new approach based on a vibration model of 1.5 degrees of freedom , 2022, Appl. Math. Comput..

[2]  Muhammad Shamrooz Aslam,et al.  Design of sliding mode controller for sensor/actuator fault with unknown input observer for satellite control system , 2021, Soft Computing.

[3]  M. S. Aslam.  L2–L∞ Control for Delayed Singular Markov Switch System with Nonlinear Actuator Faults , 2021, Int. J. Fuzzy Syst..

[4]  M. S. Aslam.  L2–L∞ Control for Delayed Singular Markov Switch System with Nonlinear Actuator Faults , 2021, International Journal of Fuzzy Systems.

[5]  Muhammad Shamrooz Aslam,et al.  Fault detection for asynchronous T–S fuzzy networked Markov jump systems with new event‐triggered scheme , 2021, IET Control Theory & Applications.

[6]  Danhong Chen,et al.  Energy analysis of a class of state-dependent switched systems with all unstable subsystems , 2020, J. Frankl. Inst..

[7]  Y. S. Hamed,et al.  Nonlinear vibrations control of a contact-mode AFM model via a time-delayed positive position feedback , 2020 .

[8]  Ian Postlethwaite,et al.  Discrete‐time adaptive control of uncertain sampled‐data systems with uncertain input delay: a reduction , 2020, IET Control Theory & Applications.

[9]  Milan Prodanovic,et al.  Full-State Feedback Control of Back-to-Back Converters Based on Differential and Common Power Concepts , 2019, IEEE Transactions on Industrial Electronics.

[10]  A. C. Carapito.  Stabilization criteria of a class of switched systems , 2019, Mathematical Methods in the Applied Sciences.

[11]  Erfan Rohadi,et al.  State-feedback control with a full-state estimator for a cart-inverted pendulum system , 2018, International Journal of Engineering & Technology.

[12]  Dmitry N. Gerasimov,et al.  Algorithms of adaptive disturbance compensation in linear systems with arbitrary input delay , 2018, Int. J. Control.

[13]  Alireza Roosta,et al.  The stability analysis of nonlinear switched systems with time delay in input and states with stable and unstable subsystems , 2018, Trans. Inst. Meas. Control.

[14]  Piyapong Niamsup,et al.  Finite-time stability of singular nonlinear switched time-delay systems: A singular value decomposition approach , 2017, J. Frankl. Inst..

[15]  Zhong-Ping Jiang,et al.  Event-based control of nonlinear systems with partial state and output feedback , 2015, Autom..

[16]  Jun Zhao,et al.  Construction of Lyapunov-Krasovskii functionals for switched nonlinear systems with input delay , 2014, Autom..

[17]  Kestutis Pyragas,et al.  A Twenty-Year Review of Time-Delay Feedback Control and Recent Developments , 2014 .

[18]  Shufeng Dong,et al.  Robust State Estimator Based on Maximum Normal Measurement Rate , 2011, IEEE Transactions on Power Systems.

[19]  Kristi A. Morgansen,et al.  Stability of Time-Delay Feedback Switched Linear Systems , 2010, IEEE Transactions on Automatic Control.

[20]  S. Chatterjee,et al.  Time-delayed absorber for controlling friction-driven vibration , 2009 .

[21]  Tianshu Bi,et al.  A novel hybrid state estimator for including synchronized phasor measurements , 2008 .

[22]  Kazuyuki Aihara,et al.  Partial state feedback control of chaotic neural network and its application , 2007 .

[23]  Xinzhi Liu,et al.  Stability of a class of linear switching systems with time delay , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  S. Pettersson.  Synthesis of switched linear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[25]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[26]  Kun Liu,et al.  Experimental study of delayed positive feedback control for a flexible beam , 2011 .

[27]  Zaihua Wang,et al.  Vibration Control via Positive Delayed Feedback , 2011 .

[28]  Leonid Mirkin,et al.  Control Issues in Systems with Loop Delays , 2005, Handbook of Networked and Embedded Control Systems.

[29]  N. C. State,et al.  Stability Analysis , 2019, Converter-Interfaced Energy Storage Systems.

[30]  H. Laborit,et al.  [Experimental study]. , 1958, Bulletin mensuel - Societe de medecine militaire francaise.