ABSTRACT The authors consider the equation αx '' (t)=-x ' (t)+F(x(t),t)-s... more ABSTRACT The authors consider the equation αx '' (t)=-x ' (t)+F(x(t),t)-signx(t-h), where F is a smooth function and α,h are positive constants. They study the dynamics of oscillations with emphasis on the existence, frequency and stability of periodic oscillations. The main conclusion of the paper is that, in the autonomous case F(x,t)≡F(x), for |F(x)|<1, there are periodic solutions with different frequencies of oscillations, though only slowly-oscillating solutions are (orbitally) stable. Also, the uniqueness of a periodic slowly-oscillating solution is shown under extra conditions, and a criterion for the existence of bounded oscillations in the case of unbounded function F(x,t) is given.
Proceedings of 35th IEEE Conference on Decision and Control, 2000
The relay control systems with time delay are considered. We show that the time delay does not al... more The relay control systems with time delay are considered. We show that the time delay does not allow to realize an ideal sliding mode, but implies oscillations, whose stability is determined by one discrete parameter-oscillation frequency. Any motion of scalar discontinuous delay system turns into a steady mode-a motion with a constant frequency. Such steady modes have all properties of
ASME 2010 Dynamic Systems and Control Conference, Volume 1, 2010
ABSTRACT A planar linearized interception problem of a maneuverable target is considered. A novel... more ABSTRACT A planar linearized interception problem of a maneuverable target is considered. A novel continuous interception strategy, based on the super-twisting second-order sliding mode control, is constructed. The sufficient conditions guaranteeing that this strategy has the maximal capture zone are established. Simulation results demonstrate that the control expenditure of the new strategy is reduced without deteriorating the homing performance in comparison with a bang-bang strategy.
ABSTRACT The authors consider the equation αx '' (t)=-x ' (t)+F(x(t),t)-s... more ABSTRACT The authors consider the equation αx '' (t)=-x ' (t)+F(x(t),t)-signx(t-h), where F is a smooth function and α,h are positive constants. They study the dynamics of oscillations with emphasis on the existence, frequency and stability of periodic oscillations. The main conclusion of the paper is that, in the autonomous case F(x,t)≡F(x), for |F(x)|<1, there are periodic solutions with different frequencies of oscillations, though only slowly-oscillating solutions are (orbitally) stable. Also, the uniqueness of a periodic slowly-oscillating solution is shown under extra conditions, and a criterion for the existence of bounded oscillations in the case of unbounded function F(x,t) is given.
Proceedings of 35th IEEE Conference on Decision and Control, 2000
The relay control systems with time delay are considered. We show that the time delay does not al... more The relay control systems with time delay are considered. We show that the time delay does not allow to realize an ideal sliding mode, but implies oscillations, whose stability is determined by one discrete parameter-oscillation frequency. Any motion of scalar discontinuous delay system turns into a steady mode-a motion with a constant frequency. Such steady modes have all properties of
ASME 2010 Dynamic Systems and Control Conference, Volume 1, 2010
ABSTRACT A planar linearized interception problem of a maneuverable target is considered. A novel... more ABSTRACT A planar linearized interception problem of a maneuverable target is considered. A novel continuous interception strategy, based on the super-twisting second-order sliding mode control, is constructed. The sufficient conditions guaranteeing that this strategy has the maximal capture zone are established. Simulation results demonstrate that the control expenditure of the new strategy is reduced without deteriorating the homing performance in comparison with a bang-bang strategy.
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Papers by Leonid Fridman