Controllability and Observability of Linear Time-Invariant Uncertain Systems Irrespective of Bounds of Uncertain Parameters

In this paper, the controllability and observability of linear time-invariant uncertain systems are investigated. The systems under consideration contain time-invariant uncertain parameters that may take arbitrarily large values. In such a situation, the locations of uncertain parameters in system matrices play an important role. We examine the permissible locations of uncertain parameters in system matrices for a linear uncertain system to be controllable and observable independently of the bounds of the uncertain parameters. The objective of this paper is to show that a linear uncertain system is controllable and observable, irrespective of the bounds of uncertain parameters, if and only if the system has a particular configuration called a complete generalized antisymmetric stepwise configuration (CGASC). Furthermore, the dual configuration of a CGASC is introduced and studied here.