On Minimum Cost Sparsest Input-Connectivity for Controllability of Linear Systems

This article deals with algorithmic techniques to ensure sparsest input-connectivity while retaining controllability of linear systems. We assume that the input matrix is constrained in the sense that the set of states that each input (if present,) can influence is known a priori, and that each interconnection between an input and a state is associated with a certain cost. In this setting we determine a set of input-connections that lead to the minimum cost and ensures that the resulting system is structurally controllable. We identify large class of systems for which these problems are solvable in polynomial time using efficient algorithms. Graph-theoretic tools are employed to solve the above class of constrained design problems. Illustrative example is included to demonstrate the efficacy of the techniques developed here.