Synthesis of discrete control systems by the method of dynamic contraction (Q1921568)

The paper is devoted to the development of methods for synthesizing discrete systems. For that purpose the method of dynamic contraction is used. Consider a control system whose behaviour is described by an equation with discrete time \[ y_k=\sum^n_{i=1} a_iy_{k-1}+\sum^n_{i=1} b_iu_{k-1}+\sum^n_{i=1} g_iw_{k-1}, \] where \(k\) means the time step, \(y\) is the measured output of the system, \(u\) is a control function, and \(w\) is some unmeasured disturbance. It is supposed moreover that \[ \sum^n_{i=1}b_i\neq 0. \] The paper contains the construction of the structure of the control law. Conditions for separability (decoupling) of the motions are obtained. Concerning the practical realization of the discrete control algorithm obtained in the paper, the author takes into account the influence of variable parameters and errors. He computes the static error and the rate error. An example contains the application of the theoretical results to a system with concrete numerical coefficients and the graphs of the system behaviour are included.