Dual invariance structure of controllability and observability

This paper investigates the controllability and the observability of linear time-invariant uncertain systems. The systems under consideration contain time-invariant uncertain parameters that may take arbitrarily large values. In this case, the locations of uncertain entries in the system matrices play an important role. The new concept of controllability and observability invariance for a linear uncertain system is defined and studied. It is shown that a linear uncertain system is controllability and observability invariant if and only if the system has a particular geometric configuration called a complete generalized antisymmetric stepwise configuration (CGASC). Furthermore, the dual structure of a CGASC is introduced and studied.