Linear Control System Can Be Distinguished In The Observability Of Hybrid Systems Applications

Further results on the properties of distinguishability about linear control systems are derived. The algebraic equivalent condition of weak distinguishability is given. The concept of "distinguishability subspace pair" is introduced, with which neces-sary condition for two linear control systems to have distinguishability subspace pair is presented. Similar to weak distinguishability, the equivalent condition for two maxi-mal observability subspaces(ie, with maximal dimensions) to form a distinguishability subspace pair is deduced. In this way, concepts of "distinguishability", "weak dis-tinguishability" as well as "disitinguishability subspace pair" are unified in the same form. Finally, using the results concerning "distinguishability subspace pair", we get some further applications in the observability of single switched linear systems by presenting the necessary and sufficient conditions for the single switched linear systems consisting of two unobservable subsystems to be observable.