Finite‐time L1 bumpless transfer control for switched positive delayed systems: A state‐dependent limited frequency switching scheme

• Published in: International journal of robust and nonlinear control Vol. 34; no. 13; pp. 9166 - 9181
• Main Authors: Wang, Peng, Lin, Pin, Zhang, Hehong, Zhao, Ying, Sang, Hong, Dimirovski, Georgi M.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.09.2024
• Subjects: bumpless transfer; Control systems design; Discontinuity; finite‐time L1$$ {L}_1 $$‐gain performance; Liapunov functions; state‐dependent switching; Subsystems; switched positive delayed systems; Switching
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7454

This work is concerned with the L1$$ {L}_1 $$ bumpless transfer control issue for switched positive delayed systems on finite horizons. A bumpless transfer input scheme and a state‐dependent limited frequency switching scheme, induced by the transient control input discontinuities during controller switching and by the frequent switching for multiple subsystems, respectively, are jointly introduced. The main advantages of the presented schemes are that the amplitude of the control input discontinuities and the frequent switches are all reduced by the dual design of bumpless transfer controllers for subsystems and a state‐dependent limited frequency switching scheme. By utilizing the multiple linear copositive Lyapunov functionals, sufficient conditions are also offered so as to achieve the desirable closed‐loop performances, including positivity, finite‐time boundedness, bumpless transfer property and a prescribed L1$$ {L}_1 $$‐gain property. Finally, a practical example is borrowed which validates the proposed schemes.