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Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Czornik Adam, Makarov Evgenii, Niezabitowski Michał, Popova Svetlana, Zaitsev Vasilii

Archives of Control Sciences

2021

Vol. 31, No. 1

81--98

Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.