A synthesis procedure for disturbance decoupling with local input-to-state stability in discrete-time switching linear systems

This work deals with disturbance decoupling in discrete-time switching linear systems. The structural decoupling problem - i.e., the mere problem of making the output insensitive to undesired inputs - is discussed first. Then, a zero-input state-stability requirement is taken into account. Quadratic stability under arbitrary switching is considered. On the one hand, this leads to a convex procedure for the synthesis of the control law. On the other hand, this guarantees global uniform asymptotic stability of the compensated system, which, in turn, implies local input-to-state stability. The discrete-time switching linear systems considered are allowed to have feedthrough terms from the control input to the output, which requires suitable generalizations of some well-known geometric notions - like, e.g., that of robust controlled invariant subspace - to be introduced. A numerical example is worked out to illustrate the devised synthesis procedure.