Controlled linear system with delayed relay output under impulse random disturbances

The paper is devoted to the first order delayed linear system with relay output controlled by the proportional-integral (PI) regulator. The deterministic system exhibits stable oscillations, and, since the system itself is stable, it can be suitable to switch off the controller if there are no disturbances during a long time interval. In the present work, the random disturbances are modelled by a Poisson stream of impulses, and the goal is to determine the instants of switching on (off) of the PI controller. After several assumptions and quantization of the time axis, we construct the new optimal control problem which is successfully solved with the help of the dynamic programming approach.     

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov–Krasovskii functionals

In this note is proposed an analogue for linear delay systems of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown that strong delay-independent stability of delay system is equivalent to the feasibility of certain linear matrix inequality (LMI), related to quadratic Lyapunov–Krasovskii functionals.     

An exact stability analysis test for single-parameter polynomially-dependent linear systems

We provide a new condition for testing the stability of a single-parameter, polynomially-dependent linear system of polynomial degree N of the form x/spl dot/=A(/spl rho/)x, A(/spl rho/)=/spl Sigma//sub i=0//sup N//spl rho//sup i/ A/sub i/ (1) over a compact interval. The test is nonconservative and can be cast as a convex feasibility problem in terms of a pair of linear matrix inequalities (LMIs).     

Lyapunov equation for the stability of linear delay systems ofretarded and neutral type

In this note, the delay-independent stability of delay systems is studied. It is shown that the strong delay-independent stability is equivalent to the feasibility of certain linear matrix inequality (LMI), that is to the existence of a quadratic Lyapunov-Krasovskii functional, independent of the (nonnegative) value of the delay. This constitutes the analogue of some well-known properties of finite-dimensional systems. This result is then applied to study delay-independent stability of systems with polytopic uncertainties     

Lyapunov Equation for the Stability of 2-D Systems

An analogue of the characterization of asymptotic stability of the 1-D systems by the solvability of associated Lyapunov equation is proposed here for 2-D systems. It is shown that internal stability of Roesser model is equivalent to the feasibility of some linear matrix inequality (LMI), related to quadratic Lyapunov functions.     

Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.     

Extension of Popov absolute stability criterion to non-autonomous systems with delays

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryless non-linearities subject to sector conditions. The proposed sufficient conditions are expressed in the frequency domain, a form well-suited for robustness issues, and lead to simple graphical interpretations for scalar systems. Apart from the usual conditions, the results assume basically a generalized sector condition on the derivative of the non-linearities with respect to time. Results for local and global stability are given, the latter concerning in particular the linear time-varying ones. For rational transfers, the frequency conditions are equivalent to some easy-tocheck linear matrix inequalities:this leads to a tractable method of numerical resolution by rational approximation of the transfer. As an illustration, a numerical example is provided.     

Backstepping design for time-delay nonlinear systems

The backstepping approach is adapted to the problem of globally uniformly asymptotically stabilizing nonlinear systems in feedback form with a delay arbitrarily large in the input. The strategy of design relies on the construction of a Lyapunov-Krasovskii functional. Continuously differentiable control laws are constructed.     

Radiative decay following low energy charge exchange collisions at the Agrippa facility

From radiative decay observed in the X and VUV domain, it is possible to determine the (n, l) substate populations and deduce their excitation cross sections. We consider here the case of different projectiles of charge +8. For some of them, we show σ_nl for single capture from H ₂ and He, as a function of energy. From the spectra it is recognized that double capture followed by radiative decay is effective. Observed transitions — of the same nature as dielectronic recombination satellites — are the signature of this process. Finally, in the case where energy levels are not known since the capture is a selective process, radiative decay appears thus as a means for basic spectroscopic studies.