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The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...
In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.
The polynomial matrix equation is solved for those and that give proper transfer functions characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly...
The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is
considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to
increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to
a related open question raised by Alabau and Komornik...
A cascade scheme for passivity-based stabilization of a wide class of nonlinear systems is proposed in this paper. Starting from the definitions and basic concepts of passivity-based stabilization via feedback (which are applicable to minimum phase nonlinear systems expressed in their normal forms) a cascade stabilization scheme is proposed for minimum and non-minimum phase nonlinear systems where the constraint of stable zero dynamics imposed by previous stabilization approaches is abandoned. Simulation...
This paper is concerned with the structure of
asymptotically
stabilizing feedbacks for a nonlinear control system
on .
We first introduce a family of discontinuous, piecewise smooth vector fields
and derive a number of properties enjoyed by
solutions of the corresponding O.D.E's.
We then define a class of “patchy feedbacks”
which are obtained by patching together a locally finite
family of smooth controls.
Our main result shows that,
if a system is asymptotically controllable at the origin,...
A global feedback control of a system that exhibits a subcritical monotonic instability
at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero
mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero
mode. The method based on a variational principle is applied for the derivation of a
low-dimensional evolution model. In the framework of this model the investigation of the
system’s dynamics...
Poisson driven stochastic differential equations on a separable Banach space are examined. Some sufficient conditions are given for the asymptotic stability of a Markov operator P corresponding to the change of distribution from jump to jump. We also give criteria for the continuous dependence of the invariant measure for P on the intensity of the Poisson process.
Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking...
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