Adaptive stabilization of impulsive switched linear time-delay systems: a piecewise dynamic gain approach. (English) Zbl 1415.93230
Summary: In the presence of discontinuous time-varying delays, neither Krasovskii nor Razumikhin techniques can be successfully applied to adaptive stabilization of uncertain switched time-delay systems. This paper develops a new adaptive control scheme for switched time-delay systems that can handle impulsive behavior in both states and time-varying delays. The core of the proposed scheme is a Lyapunov function with a dynamically time-varying coefficient, which allows the Lyapunov function to be non-increasing at the switching instants. The control scheme, guaranteeing global uniformly ultimate boundedness of the closed-loop system, substantially enlarges the class of uncertain switched systems for which the adaptive stabilization problem can be solved. A two-tank system is used to illustrate the effectiveness of the method.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C40 | Adaptive control/observation systems |
| 93C05 | Linear systems in control theory |
Keywords:
adaptive control; impulsive switched linear systems; time-varying delays; mode-dependent dwell timeReferences:
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