Results 301 to 310 of about 276,545 (338)

Stability and exponential stability in linear viscoelasticity

Milan Journal of Mathematics, 2009
In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation $${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$$
openaire   +3 more sources

Exponential Stability With RISE Controllers

IEEE Control Systems Letters, 2022
A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that are subject to sufficiently smooth bounded exogenous ...
Omkar Sudhir Patil, Axton Isaly, Bin Xian, Warren E. Dixon   +3 more
openaire   +2 more sources

Exponential stability revisited

International Journal of Control, 1987
Relationships between asymptotic stability and exponential stability are investigated. It is shown that asymptotically stable but not exponentially stable non-linear systems are structurally unstable and hence of little practical interest.
openaire   +2 more sources

On the exponential stability of discrete volterra systems

Journal of Difference Equations and Applications, 2000
In this paper necessary and sufficient conditions for the exponential stability of discrete linear Volterra systems are proved.
CRISCI M. R., KOLMANOVSKII V. B., RUSSO, ELVIRA, VECCHIO A.   +3 more
openaire   +4 more sources

Nonuniform exponential stability and admissibility

Linear and Multilinear Algebra, 2015
For cocycles defined by sequences of linear operators in a Banach space, we study the relation between the notions of nonuniform exponential stability and admissibility. The latter refers to the existence of bounded solutions for any bounded nonlinear perturbation of the original cocycle.
Claudia Valls, Luis Barreira
openaire   +2 more sources

Equivalence of input-output stability and exponential stability

Systems & Control Letters, 1989
Abstract For a large class of well-posed infinite-dimensional systems we show that if their state space realisation is exponentially stabilizable and detectable, then exponential stability of the system operator is equivalent to input-output stability.
openaire   +3 more sources

Exponential stabilization of the rolling sphere

Automatica, 2004
In this paper we present a non-smooth controller for exponential stabilization of the sphere. This has remained an open problem despite significant progress in nonholonomic systems. Our control design is based on inputs in a rotating coordinate frame that individually produce primitive motions of the sphere along straight lines and circular arcs.
Tuhin Das, Ranjan Mukherjee
openaire   +2 more sources

Uniform exponential stability

1996
In this chapter we shall study the uniform growth bound ω0(T) in more detail. Our main concern is finding necessary and sufficient conditions for uniform exponential stability.
openaire   +2 more sources

Mean square exponential stability

2009
The problem of mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. Four different definitions of the concept of exponential stability in the mean square are introduced and it is shown that they are not always equivalent.
Vasile Dragan, Toader Morozan, Adrian-Mihail Stoica   +2 more
openaire   +2 more sources

Stability of an exponentially stabilizable system

IEEE Transactions on Automatic Control, 1984
Let A be the generator of a C 0 semigroup T(t), t \geq 0 , and denote by S(t), t \geq 0 , the semigroup generated by A - K , where K is a bounded linear operator on a Hilbert space. In this note we find necessary and sufficient conditions for the original semigroup T(t), t \geq 0 , to be exponentially stable, given that the "feedback" semigroup S(t), t
openaire   +2 more sources