Dual-Mode-Transition-Dependent Smooth Control for Switched Linear Systems

This paper explores the issue of smooth control of continuous-time switched linear systems. The dual-mode-dependent stabilizing controller is employed instead of the mode-dependent controller used in the existing smooth control results, such that the control freedom is increased and the admissible dual-modal average dwell time switching is generated to enhance the switching frequency of mode-dependent or admissible edge-dependent average dwell-time switching. To eliminate the control input bumps caused by switching controllers, a new dual-mode-transition-dependent smooth control method is proposed by using the time-interpolated controller operating across the front and back subsystems. Unlike existing smooth control methods, the operation of pre-designed controller gain is avoided and the problem of system instability during the transition stage is greatly mitigated or overcome by the proposed method, such that the control performance and the admissible switching frequency are significantly improved. Two examples are presented to illustrate the benefits of the obtained theoretical results.