DEPENDENCE UPON INITIAL CONDITIONS AND PARAMETER OF SOLUTIONS OF IMPULSIVE DIFFERENTIAL-EQUATIONS WITH VARIABLE STRUCTURE

A class of impulsive ordinary differential equations with variable structure is introduced. For the equations of this class it is characteristic that the changes of their right-hand sides and the impulses are realized at the moments when their solutions nullify switching functions (special functions with domains of definition coinciding with the phase space of the equations of the class). The initial value problem (with a parameter and without a parameter) for equations with variable structure and impulses is considered. Sufficient conditions for continuability and continuous dependence on the initial conditions and a parameter of their solutions are found. By means of the equations of this class the work of a hydraulic safety valve is simulated. The results obtained are used for the qualitative investigation of the model. © 1990 Plenum Publishing Corporation.