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We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer...
We investigate stochastic averaging on infinite time interval for a class of continuous-time nonlinear systems with stochastic perturbation and remove several restrictions present in existing results: global Lipschitzness of the nonlinear vector field, equilibrium preservation under the stochastic perturbation, and compactness of the state space of the perturbation process. If an equilibrium of the...
Necessary and sufficient stability conditions are given for the existence of a continuous Lyapunov function for a semicontinuous, stochastic discrete-time system. The continuity of the Lyapunov function is linked to robustness of the stability property, which reduces to classical stability plus convergence for deterministic systems. The nature of the Lyapunov results are inspired by Lyapunov results...
In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ??n. We propose a gradient based control law which achieves exponential...
The goal of this work is to stabilize the shape and orientation of formations of N identical and fully actuated agents, each governed by double-integrator dynamics. Using stability and rigidity properties inherent to tensegrity structures, we first design a tensegrity-based, globally exponentially stable control law in one dimension. This stabilizes given inter-agent spacing along the line, thereby...
This work proposes a control law for the robot joint trajectory tracking in free space that achieves a prescribed performance of the joint position error under parametric uncertainties; the control law is extended for the case of bounded disturbances. A performance function incorporating predefined performance indices is used to produce a transformed error that is injected in the controller. Furthermore,...
In this paper, periodic learning control is presented for deterministic periodic auto-regressive exogenous systems. The control problem is approached in a certainty equivalence framework, of which a periodic learning identification algorithm is formed to estimate the periodic time-varying parameters, and the only prior knowledge is the periodicity. The learning algorithm updates the estimates periodically,...
In this paper, a generalized model of fuzzy cellular neural networks (FCNNs) with time-varying delays and impulses is formulated and investigated. By employing the delay differential inequality with impulses initial conditions and the M-matrix theory, some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for FCNNs with time-varying...
This paper considers the stability properties of a class of nonlinear singularly perturbed systems which contain marginally stable boundary layer systems. Conditions are given which guarantee that these systems are globally uniformly exponentially stable. The results are illustrated by application to control design for a flexible mechanical system.
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