Guaranteed Cost Sliding Mode Control of Switched Systems with Known Sojourn Probabilities

다국어 초록 (Multilingual Abstract)

This paper investigates the problem of the optimal guaranteed cost sliding mode control (SMC) for a class of uncertain switched systems, in which the sojourn probabilities staying in each subsystem are available. By introducing a set of stochastic variables, a new type of switched system model with known sojourn probabilities is constructed. And then, the SMC law is synthesized such that the reachability of the specified common sliding surface can be ensured. Moreover, some sufficient conditions are derived to ensure the mean-square stability of the closed-loop system with quadratic guaranteed cost function. The optimal solution of the guaranteed SMC scheme is established for the closed-loop systems. Finally, a numerical example is provided to illustrate the proposed method.

참고문헌 (Reference)

1 D. Liberzon, "Switching in Systems and Control" Springer Science & Business Media 2012

2 H. Trinh, "Switching design for suboptimal guaranteed cost control of 2-D nonlinear switched systems in the Roesser model" 24 : 45-57, 2017

3 X. Zhao, "Stability of switched positive linear systems with average dwell time switching" 48 (48): 1132-1137, 2012

4 X. Su, "Sliding mode control of discrete-time switched systems with repeated scalar nonlinearities" 62 (62): 4604-4610, 2017

5 B. Zheng, "Sliding mode control design for linear systems subject to quantization parameter mismatch" 353 (353): 37-53, 2016

6 E. Tian, "Robust H¥ control for switched systems with input delays: A sojourn-probabilitydependent method" 283 : 22-35, 2014

7 Guang-Deng Zong, "Robust Finite-time Guaranteed Cost Control for Impulsive Switched Systems with Time-varying Delay" 제어·로봇·시스템학회 15 (15): 113-121, 2017

8 L. Rodrigues, "Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization" 54 (54): 835-853, 2005

9 Wenhai Qi, "Passivity and Passification for Stochastic Systems with Markovian Switching and Generally Uncertain Transition Rates" 제어·로봇·시스템학회 15 (15): 2174-2181, 2017

10 L. Gurvits, "On the stability of switched positive linear systems" 52 (52): 1099-1103, 2007

11 Y. Li, "New criteria for exponential stability of switched time-varying systems with delays and nonlinear disturbances" 26 : 284-291, 2017

12 M. Kalidass, "H∞filtering for impulsive networked control systems with random packet dropouts and randomly occurring nonlinearities" 25 (25): 1767-1782, 2015

13 E. Tian, "H∞ filtering for discrete-time switched systems with known sojourn probabilities measurements" 60 (60): 2446-2451, 2015

14 J. Song, "Fuzzy remote tracking control for randomly varying local nonlinear models under fading and missing measurements" 26 (26): 1125-1137, 2017

15 W. Qi, "Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay" 48 (48): 2967-2975, 2017

16 H. Zhao, "Finite-time output feedback control of uncertain switched systems via sliding mode design" 49 (49): 984-996, 2018

17 A. Elahi, "Finite-time H∞ control of uncertain networked control systems with randomly varying communication delays" 69 : 65-88, 2017

18 H. Dong, "Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization" 52 : 355-362, 2015

19 H. Ren, "Event-triggered finite-time control for networked switched linear systems with asynchronous switching" PP (PP): 1-11, 2018

20 E. Hernandez-Vargas, "Discrete-time control for switched positive systems with application to mitigating viral escape" 21 (21): 1093-1111, 2011

21 Y. Niu, "Design of sliding mode control subject to packet losses" 55 (55): 2623-2628, 2010

22 R. Galv´an-Guerra, "Continuous output integral sliding mode control for switched linear systems" 22 : 284-305, 2016

23 J. Song, "Asynchronous sliding mode control of Markovian jump systems with time-varying delays and partly accessible mode detection probabilities" 93 : 33-41, 2018

24 Y. Liu, "Adaptive sliding mode reliable control for switched systems with actuator degradation" 9 (9): 1197-1204, 2015

25 T. Yuno, "A sufficient condition for the stability of discrete-time systems with state-dependent coefficient matrices" 59 (59): 243-248, 2014

26 E. Tian, "A new state feedback H∞ control of networked control systems with time-varying network conditions" 349 (349): 891-914, 2012