620,991 research outputs found
New summation inequalities and their applications to discrete-time delay systems
This paper provides new summation inequalities in both single and double
forms to be used in stability analysis of discrete-time systems with
time-varying delays. The potential capability of the newly derived inequalities
is demonstrated by establishing less conservative stability conditions for a
class of linear discrete-time systems with an interval time-varying delay in
the framework of linear matrix inequalities. The effectiveness and least
conservativeness of the derived stability conditions are shown by academic and
practical examples.Comment: 15 pages, 01 figur
On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems
In this paper, we study the problem of robust stabilization for linear
time-varying (LTV) systems subject to time-varying normalized coprime factor
uncertainty. Operator theoretic results which generalize similar results known
to hold for linear time-invariant (infinite-dimensional) systems are developed.
In particular, we compute an upper bound for the maximal achievable stability
margin under TV normalized coprime factor uncertainty in terms of the norm of
an operator with a time-varying Hankel structure. We point to a necessary and
sufficient condition which guarantees compactness of the TV Hankel operator,
and in which case singular values and vectors can be used to compute the
time-varying stability margin and TV controller. A connection between robust
stabilization for LTV systems and an Operator Corona Theorem is also pointed
out.Comment: 20 page
Robust stability of non linear time varying systems
summary:Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided
Stability and robustness of slowly time-varying linear systems
"August 1987." Caption title. Text printed in double columns.Includes bibliographical references.Supported in part by a grant from the NASA Ames and Langley Research Centers, NASA/NAG 2-297Jeff S. Shamma and Michael Athans
On the stability of some linear nonautonomous systems
Stability of linear nonautonomous systems described by differential equations with time varying coefficient
The converse of the passivity and small-gain theorems for input-output maps
We prove the following converse of the passivity theorem. Consider a causal
system given by a sum of a linear time-invariant and a passive linear
time-varying input-output map. Then, in order to guarantee stability (in the
sense of finite L2-gain) of the feedback interconnection of the system with an
arbitrary nonlinear output strictly passive system, the given system must
itself be output strictly passive. The proof is based on the S-procedure
lossless theorem. We discuss the importance of this result for the control of
systems interacting with an output strictly passive, but otherwise completely
unknown, environment. Similarly, we prove the necessity of the small-gain
condition for closed-loop stability of certain time-varying systems, extending
the well-known necessity result in linear robust control.Comment: 15 pages, 3 figure
Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics
This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value Ό. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations
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