Improving the performance of low-gain designs for bounded control of linear systems

An online scheduling of the parameter ensuring in addition to closed loop stability was presented. Attention was given to saturated linear low-gain control laws. Null controllability of the considered linear systems was assumed. The family of low gain control laws achieved semiglobal stabilization.

Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Instability of the steady-state regime of generation in laser diodes with a broad gain spectrum

The laser-diode parameters at which the steady-state regime of generation becomes unstable are analyzed within the framework of the mode-locking model. The crucial role of the transverse inhomogeneity of the field, pumping intensity, and spectrum width in developing the instabilities of the steady-state regime of generation is demonstrated. The calculated values of the instability threshold are shown to be consistent with the experimental results. © 2008 Springer Science+Business Media, Inc.

Role of a high gain of the medium in superradiance generation and in observation of coherent effects in semiconductor lasers

A theoretical model of superradiant pulse generation in semiconductor laser structures is developed. It is shown that a high optical gain of the medium can overcome phase relaxation and results in a built-up superradiant state (macroscopic dipole) in an assembly of electron - hole pairs on a time scale much longer than the characteristic polarisation relaxation time T2. A criterion of the superradiance generation is the condition acmT2 > 1, where α is the gain coefficient and cm is the speed of light in the medium. The theoretical model describes both qualitatively and quantitatively the author's own experimental results.