Dissipativity Criterion for Linear Systems with a Coupling Delay and Asymptotically Positive Realness Constraint

In this work, a robust stabilizability condition for discrete-time interconnected systems is derived from the quadratically delay-robust dissipativity of the open-loop subsystems and the asymptotically positive realness constraint (APRC) presented previously. Linear interconnections with a single coupling delay element and persistent input disturbances are the essences of this development. A globally robust stabilizable invariant set for the coupling delayed system subject to state and input constraints is considered and incorporated into the quadratic dissipativity criteria. For application, the APRC is subsequently converted into a convex stability constraint for the local MPC optimization. Stability constraints are artificial constraints adding to the optimization problem of MPC solely for the stability assurance purpose.