二次不变子空间约束下的同时强镇定控制器

Within the framework of nest algebra, this paper studies the existence of strongly stabilizing and simultaneously strongly stabilizing controllers for linear time-varying systems based on quadratically invariant subspace constraints, using bicoprime factorization methods. This paper provides new theories for the design of linear systems. Based on bicoprime factorization, we focus on two related linear time-varying systems as our main research objects to study the strongly stabilizing controllers for a single linear system. Lastly, we provide a criterion for the existence of simultaneously strongly stabilizing controllers for two systems, in terms of bicoprime factorization of the system.