In general Q and R are given, and ideally M is desired to be as large
as possible. As far as the three parameters N, D and L there is a
trade-off in selecting their values. Large N values lead to superfluous
controller switchings which may destabilize the system;
small N typically leads to a slow-responding system thus
hindering its performance. Large values of D increase the system’s
stability margin while decreasing the system’s bandwidth (due to
the need to simultaneously stabilize a large number of systems).
The parameter L directly affects the speed of the system’s
response. From a performance point of view, large L values are
desired; however, this may lead to an infeasibility issue in the
controller design.
It should be noted that a judicious selection of these
parameters is desired, since there are contradicting outcomes
behind their selection. As an example, large values of N lead to a
faster performance at the expense of causing significant switchings
caused by the transition of the controller’s operating regime.
Similarly, large values of D increase the systems’s stability margin
at the expense of decreasing its bandwidth which is also affected
by the parameter L.
Practical considerations ask for an a priori selection of N and D
while computing the largest L that generates a feasible controller.
This increase of the value of the value of L will result in a faster
system response. From an algorithmic point of view the ‘‘fast’’
stabilizing controller for the |th region can be computed in a
similar manner from (8) as