24,432 research outputs found
A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections
A general ISS-type small-gain result is presented. It specializes to a
small-gain theorem for ISS operators, and it also recovers the classical
statement for ISS systems in state-space form. In addition, we highlight
applications to incrementally stable systems, detectable systems, and to
interconnections of stable systems.Comment: 16 pages, no figure
Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations
Lyapunov-like characterizations for non-uniform in time and uniform robust
global asymptotic stability of uncertain systems described by retarded
functional differential equations are provided
Robustness of controllers designed using Galerkin type approximations
One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme
Input to State Stability of Bipedal Walking Robots: Application to DURUS
Bipedal robots are a prime example of systems which exhibit highly nonlinear
dynamics, underactuation, and undergo complex dissipative impacts. This paper
discusses methods used to overcome a wide variety of uncertainties, with the
end result being stable bipedal walking. The principal contribution of this
paper is to establish sufficiency conditions for yielding input to state stable
(ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and
phase-based uncertainties. In particular, it will be shown formally that
exponential input to state stabilization (e-ISS) of the continuous dynamics,
and hybrid invariance conditions are enough to realize stable walking in the
23-DOF bipedal robot DURUS. This main result will be supported through
successful and sustained walking of the bipedal robot DURUS in a laboratory
environment.Comment: 16 pages, 10 figure
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