The Study Of Some Problems For Impulsive Control Systems

The short temporary perturbation is commonly encountered in many evo-lutionary processes, for example, biological phenomena involving thresholds,bursting rhythm models in pathology, optimal control of economic systems,frequency-modulated signal processing systems. Impulsive differential systemsprovide a natural description of observed evolutionary processes with impulseeffect. In this thesis, the problems of the impulsive control systems are in-vestigated. In the second chapter, the problems of robust stability, robuststabilization and robust H_∞control for uncertain impulsive linear systems areinvestigated. The parametric uncertainties are assumed to be time-varying andnorm-bounded. The sufficient conditions for above problems are developed interms of linear matrix inequalities. This method is helpful to improve theexisting technologies used in the analysis and control for uncertain impulsivesystems. In the third chapter, the guaranteed cost control problem for uncer-tain Lur'e systems with norm-bounded time-varying parametric uncertaintiesis investigated. We introduce a quadratic cost index for the impulsive con-trolled Lur'e systems. The sufficient conditions for the existence of guaranteedcost controller and the minimum upper of the quadratic cost index are derivedin terms of linear matrix inequalities. In the fourth chapter, impulsive controlis applied to uncertain impulsive switched systems. The sufficient conditionsof robust stability, robust stabilization and robust H_∞control for the impul-sive switching systems are derived in terms of linear matrix inequalities. Theconclusions in this thesis are in form of linear matrix inequalities, and can beeasily verified in the actual operation. Numerical examples are provided to demonstrate the effectiveness and applicability of the conclusions.