Interval Observer-based Feedback Control for Rehabilitation in Tremor

Tremor, one of the most common health disorders, is defined as a chronic movement disorder. To reduce tremor in patients, the design of stabilizing techniques is critical. For this purpose, we consider an uncertain continuous-time linear time-varying oscillator model of tremor in this article. We design a state feedback control for deep brain stimulation technique by considering the practical case in which only sets of admissible values are given for the nominal values of the stimulation amplitude, the time-varying tremor's angular frequency and the tremor measurement noise. First, we estimate state signal bounds that include the true unknown value of the state. Next, we design a stabilizing control input based on the estimated bounds. The stability of the controlled system is verified using linear matrix inequalities (LMIs). We demonstrate the methodology's performance in numerical simulations.