POLE PLACEMENT OF LINEAR MULTI-VARIABLE TIME-VARYING DISCRETE NON-LEXICOGRAPHICALLY-FIXED SYSTEMS
This paper concerns the pole placement control design method for linear time-varying discrete multivariable systems.
The method can be regarded as "a discrete Ackermann-like algorithm".
The basic problem is to find a time-varying state feedback gain for linear time-varying discrete systems,
so that the closed loop system is equivalent to some time-invariant system with desired constant closed loop poles.
For this purpose, we focus the relative degrees of the multi-variable plant.
It will be shown that the pole placement controller can be derived simply by finding some particular "output signal" such that the relative degree from the input to this output is equal to the order of the system.
Then, the feedback gain vector can be calculated directly from the system parameters without transforming the system into any standard form.
An other property of the time-varying system is that the reachability (controllability) indices might be variable.
Such a system is called a non-lexicographially-fixed system.
For continuous systems,
N.Olgac et.al. discussed this problem,
and proposed one design method by augmenting the original system.
Here, we use this idea for multivariable discrete systems, and propose the new design method of the pole placement state feedback.