Regions of guaranteed cost for LMI-based robust model predictive controllers for systems with uncertain input delay

This paper is concerned with the performance of LMI-based robust model predictive controllers (RMPC) designed for systems with uncertain time delay. Such an uncertainty can be associated, for instance, to unpredictable changes in operating conditions, failures in the system components or reconfigurations in communication links. More specifically, the investigation involves the determination of “regions of guaranteed cost” D̅^γ, defined as the set of feasible initial state conditions for which the resulting cost function is not greater than a given value̅γ. These regions are characterized by using a recently proposed technique in which an inner approximation of D̅^γ is generated as the convex hull of extreme points determined through the solution of a modified version of the RMPC optimization problem. For illustration, a numerical simulation model of an angular positioning system with input delay is employed. The results reveal that the presence of delay causes a loss of performance, in that D̅^γ becomes smaller for a given guaranteed cost̅γ. This issue is further aggravated if the delay is uncertain, since the control law becomes more conservative.