Reduced-order Observers Design for Unknown Inputs Switched Systems without Strongly Detectable of Subsystems

This paper investigates the reduced-order switched observers for switched linear systems with unknown inputs when none subsystems are strongly detectable under dwell time switching. A time-varying disturbance-decoupling state coordinate transformation is first utilized to decouples the unknown input from a subset of the transformed state coordinates. Secondly, a linear coordinate transformation is constructed to decompose the system state into directly available state component parts and non-direct available state component parts. The existence conditions of the reduced-order switched observers are derived by both restricting the upper bounds and the lower bounds of dwell time, decreasing the energy of switched systems at switching times, and confining the growth of subsystems' Lyapunov functions, and the reduced-order switched observers are constructed. Stability analysis of switched error dynamics is also presented. Then, the proposed reduced-order switched observers asymptotically converges to the state under the designed dwell time switching signal. Finally, an example confirms the effectiveness of the proposed method.