Persistence filter-based control for systems with time-varying control gains

The paper addresses the generic problem of devising stabilizing control laws for systems with time-varying control gains and unstable drift terms. Specifically, a large class of single-input, linear, control affine systems are considered wherein the control gains (coefficients) can become singular at certain instants in time or stay singular for large time intervals, thus amounting to pointwise-in-time loss of controllability. The time-varying components of the control gains are assumed to be sufficiently smooth and possess certain structure expressed in terms of persistent excitation conditions. A novel persistence filter construction is developed which helps achieve stabilization objectives. Some preliminary results on bounded trajectory tracking are also provided.