1,718 research outputs found
Input-Output-to-State Stability
This work explores Lyapunov characterizations of the input-output-to-state
stability (IOSS) property for nonlinear systems. The notion of IOSS is a
natural generalization of the standard zero-detectability property used in the
linear case. The main contribution of this work is to establish a complete
equivalence between the input-output-to-state stability property and the
existence of a certain type of smooth Lyapunov function. As corollaries, one
shows the existence of ``norm-estimators'', and obtains characterizations of
nonlinear detectability in terms of relative stability and of finite-energy
estimates.Comment: Many related papers can be found in:
http://www.math.rutgers.edu/~sonta
Backstepping controller synthesis and characterizations of incremental stability
Incremental stability is a property of dynamical and control systems,
requiring the uniform asymptotic stability of every trajectory, rather than
that of an equilibrium point or a particular time-varying trajectory. Similarly
to stability, Lyapunov functions and contraction metrics play important roles
in the study of incremental stability. In this paper, we provide
characterizations and descriptions of incremental stability in terms of
existence of coordinate-invariant notions of incremental Lyapunov functions and
contraction metrics, respectively. Most design techniques providing controllers
rendering control systems incrementally stable have two main drawbacks: they
can only be applied to control systems in either parametric-strict-feedback or
strict-feedback form, and they require these control systems to be smooth. In
this paper, we propose a design technique that is applicable to larger classes
of (not necessarily smooth) control systems. Moreover, we propose a recursive
way of constructing contraction metrics (for smooth control systems) and
incremental Lyapunov functions which have been identified as a key tool
enabling the construction of finite abstractions of nonlinear control systems,
the approximation of stochastic hybrid systems, source-code model checking for
nonlinear dynamical systems and so on. The effectiveness of the proposed
results in this paper is illustrated by synthesizing a controller rendering a
non-smooth control system incrementally stable as well as constructing its
finite abstraction, using the computed incremental Lyapunov function.Comment: 23 pages, 2 figure
Notions of Input to Output Stability
This paper deals with several related notions of output stability with
respect to inputs. The inputs may be thought of as disturbances; when there are
no inputs, one obtains generalizations of the classical concepts of partial
stability. The main notion studied is called input to output stability (IOS),
and it reduces to input to state stability (ISS) when the output equals the
complete state. Several variants, which formalize in different manners the
transient behavior, are introduced. The main results provide a comparison among
these notions. A companion paper establishes necessary and sufficient
Lyapunov-theoretic characterizations.Comment: 16 pages See http://www.math.rutgers.edu/~sontag/ for many related
paper
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