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Computation and stability of limit cycles in hybrid systems. (English) Zbl 1096.34020
An algorithm for the investigation of limit cycles in hybrid systems is suggested. A Newton-based procedure allows one to compute initial conditions and switching instants which are used to simulate a limit cycle. Furthermore, stability properties of the limit cycle can be studied by using the eigenvalues of the Jacobian matrix for the linearized system which are computed during the run. The sensitivity of the cycle with respect to the change of a control parameter introduced in the original system is also investigated. An algorithm is applied to a phase-locked loop problem to demonstrate its advantages over a fixed-point method.
MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34A36Discontinuous equations
93C57Sampled-data control systems
34A45Theoretical approximation of solutions of ODE