Geometric Methods and Computational Tools for Switching Structured Linear Systems

This work deals with switching structured linear systems, a class of structured linear systems whose existing links between the state, input, and output variables have unknown numerical values and, in addition, are subject to change according to an exogenous, time-dependent signal. Geometric methods and computational tools developed to solve control and observation problems stated for this class of structured linear systems are presented. In particular, this work delves into the notions of invariance, controlled invariance, and conditioned invariance and focuses on their use in the statement and proof of conditions for the solvability of the disturbance decoupling problem, both by state feedback and by output feedback, and of the unknown-input state observation problem. The fundamental concepts and the main results are explained using handy examples, with visual aid provided by directed graphs.