Technical communiqueGlobal stabilization of nonlinear systems via hybrid implementation of dynamic continuous-time local controllers☆
Section snippets
Introduction and preliminaries
Consider a nonlinear system described by the equation where denotes the state, is the control input and the mapping is assumed to be for some sufficiently large . Suppose, in addition, that , namely the origin is an equilibrium point of the unforced system.
Definition 1 Consider the nonlinear system with state , , where the mappings , , and , , are in . Then, system (2) is a globally
Hybrid implementation of dynamic continuous-time controllers
In this section we discuss a control design technique – based on the knowledge of a locally stabilizing controller for system (1) – that guarantees global convergence. Moreover, we formalize the notion of hybrid implementation of the dynamic control law (2).
Assumption 1 A locally stabilizing controller of the form of (2), together with the underlying functions and , is given for (1).
To provide a concise statement of the results, let for any , and
Numerical simulations
To corroborate the above theoretical analysis, in this section, we present two examples of application of the hybrid implementation of local controllers.
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The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tingshu Hu under the direction of Editor André L. Tits.