Implicit control law for linear time varying SISO systems with bounded disturbances

We propose a linear time invariant control law for a following linear time varying SISO system. The aim of this linear time invariant control law is to obtain a linear time invariant SISO closed loop system without disturbance and with desirable dynamics. The control scheme is developed in three steps: (i) we find first a trivial control law for a controllable state realization; (ii) we find next a practical approximation of the trivial control law which guarantees internal stability and tends to the ideal behavior (obtained with the trivial control law); we assume in this second step that the state is measurable; (iii) finally we suppose that the state is not available and we thus add a state reconstructor which preserves the nice characteristics of the practical control law.