Research On Performance And Control Strategies Of Several Kinds Of Switching Systems

Over past decades,switching systems are aroused wide attention from system engineers,computer scientists and mathematicians.It comprises several subsystems described in a set of differential or difference equations and a switching signal.Switches are performed between subsystems to control according to the given switching strategy.Theories on it have been developed and improved along with the control theory.Never the less,switching systems always show complex dynamic behavior owing to the interactions between continuous dynamic systems and discrete dynamic systems.Thus,it is valuable to study on it both theoretically and practically.The paper mainly includes the following contents:(1)Polar coordinate transformation was performed on the two-dimensional linear switching system and state space angle area method was designed.The state space of two-dimensional linear switching systems was divided into angular regions with specified properties through this method.Stability and asymptotic stability of the system under any switching rules were analyzed using the state of the system trajectory in each region of the movement;Switching rules to keep the subsystems as well as the whole system stable were also investigated when each subsystem is unstable.(2)The structural characteristics of two-dimensional generalized switching systems were analyzed.The system was transformed into a simple or special form to study on by applying the finite equivalent transformation of two-dimensional generalized switched systems.The regularity,pulsed nature as well as asymptotic stability of generalized systems were discussed according to the characteristics of the elements in the transformed coefficient matrix.Strict proofs of the relevant theorem were also given.A special kind of generalized system was defined as zero-setting subsystem and partial zero-setting subsystem in the mean while and the subspace of these kind of subsystem was explored.