Loading [MathJax]/extensions/MathZoom.js
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers with increasing regions of attraction is that, when the region of attraction is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some...
Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system...
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for...
The concepts of stability, attractivity and asymptotic stability
for systems subject to restrictions of the input values are introduced
and analyzed in terms of Lyapunov functions. A comparison
with the well known input-to-state stability property introduced
by Sontag is provided. We use these concepts in order to derive
sufficient conditions for global stabilization for triangular and
feedforward systems by means of saturated bounded feedback controllers
and also recover some recent results...
We consider the system
(ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...
We consider one-dimensional affine control systems. We show
that if such a system is stabilizable by means of a continuous, time-invariant
feedback, then it can be made input-to-state stable with
respect to measurement disturbances, using a continuous,
periodic time-varying feedback. We provide counter-examples showing
that the result does not generally hold if we want the feedback to be time-invariant
or if the control system is not supposed affine.
This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of
either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant
linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...
Currently displaying 1 –
20 of
26