Decentralized and distributed robust control invariance for constrained linear systems

In this paper we propose an efficient procedure to compute time-varying Robust Control Invariant (RCI) sets for large-scale systems arising from the interconnection of M Linear Time-Invariant (LTI) constrained subsystems. In particular, the associated state-feedback controllers are nonlinear and decentralized or distributed. Our algorithm is structured in three stages: the computation of a Control Invariant (CI) set for each subsystem, the design of coupling attenuation control terms and the construction of a family or RCI sets for the overall system affected by disturbances. The last stage, which is based on the notion of practical invariance, is the only one requiring centralized computations for analyzing the stability of an M-th order system. Differently from existing approaches based on Linear Matrix Inequalities (LMIs), in case of polytopic constraints our method requires to solve local Linear Programming (LP) problems.