On controllability and observability of multichannel automatic control systems in the synthesis by the modal method using the polynomial matrix decomposition of the object and controller

When considering the issue of synthesis an automatic control system by a modular method using polynomial decomposition transfer functions object and controller, algorithms for fully controlled systems are proposed. However, question arises about possibilities this algorithm if condition is not met. The consideration is-sue turned out to be especially relevant multichannel models objects with non-square function (having unequal number input output channels). It shown that some fundamental terms theory control, such as controllability, reachability, observability, stability others, there special definitions them in case type objects. term non‒square proposed use, which used mainly foreign literature. Some restrictions on modal regulators matrix separation regulator considered. Examples internally asymptotically unstable given. A hypothesis put forward system. An example "inverted pendulum cart" considered, (in example, actions less than parameters). Using static characteristics object, it demonstrated always can stabilized given position. For setting desired angle inverted other zero, impossible hold position cart coordinate. At same time, you set at equilibrium point pendulum, then stabilization coordinate becomes possible.