Nonlinear switched systems with state dependent dwell-time

Abstract

The asymptotic convergence of nonlinear switched systems in the presence of disturbances is studied in this paper. The system switches among a family of integral input-testate stable systems. The time between two consecutive switchings is not less than a value m. This dwell-time TD is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwelltime function which depends on the comparison functions which characterize the integral input-testate stability and guarantees the state of the switched system to converge to zero under the action of disturbances with "bounded energy". The main feature of the analysis is that it does not rely on the property that the switching stops in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail.A successful strategy to deal with a largely uncertain system, whose model is unknown but belongs to one of many families of nominal (and known) models, is to design a controller for each family of possible models, and then let a supervision logic decide from time to time what is the better controller to place in the feedback loop. This control strategy is typically known as switching or logic-based or supervisory control ([14], [E], [16], [12], 171, [lo], [SI, [ll]). The study of a logicbased supervisory control system usually boils down to the analysis of the "convergence" properties' of a switched system, which depends on the piecewise constant switching signal U generated by the supervision ''Convergence to zero of (nonlinear timevarying) systems with disturbances is a fundamental issue which arises not only in (switching) adaptive control, but a150 in many other control problems. See [ZO] for other results in this regard. 0-7803-7516-5/02/$17.00 02002 IEEE

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