  A generalization of canonical quantization which maps a dynamical operator to
a dynamical superoperator is suggested. Weyl quantization of dynamical
operator, which cannot be represented as Poisson bracket with some function, is
considered. The usual Weyl quantization of observables is a specific case of
suggested quantization. This approach allows to define consistent quantization
procedure for non-Hamiltonian and dissipative systems. Examples of the harmonic
oscillator with friction (generalized Lorenz-Rossler-Leipnik-Newton equation),
the Fokker-Planck-type system and Lorenz-type system are considered.
