Stabilization of time-varying systems is a non-trivial problem. The control of time-varying systems is complicated by the fact that the stability properties of the system cannot be determined by the frozen-time system eigenvalues [1]. Some controllers require explicit knowledge of the time variation of the system parameters for control synthesis [2, 3, 4]. In addition, some control strategies require a sufficiently small rate of time variation in order to guarantee stability [5]. The stability of systems with periodic time variation is analyzed in detail in [6]. In this paper we consider the problem of adaptive stabilization for a class of second-order time-varying systems under full-state feedback. Interpreting the system states as position and velocity, the system is assumed to have unknown, time-varying damping and stiffness coefficients, which are assumed only to be piecewise continuous and bounded. Furthermore, these bounds need not be known. The novel aspect of the controller is the fact that global convergence is guaranteed under non-parametric assumptions about the time-variation. In [7] the controller presented in this paper is applied to second-order nonlinear plants with position-dependent stiffness and damping coefficients. Related theory and references to relevant adaptive control literature can be found in [7] and in [8], where the stability of the closed-loop system is proven for linear time-invariant plants.
展开▼
