Vijaya Sekhar Chellaboina

Resetting virtual absorbers for vibration control

A novel class of controllers, called resetting virtual absorbers, is proposed as a means for achieving energy dissipation. A general framework for analyzing resetting virtual absorbers is given, and stability of the closed-loop system is analyzed. Special cases of resetting virtual absorbers, called the virtual trap-door absorber and the virtual one-way absorber, are described, and some illustrative examples are given.

Guaranteed domains of attraction for multivariable Luré systems via open Lyapunov surfaces

SUMMARY In this paper we provide guaranteed stability regions for multivariable Lure« -type systems. Specifically, using the Lure« —Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti-windup controllers for systems subject to input saturation. ( 1997 by John Wiley & Sons, Ltd.

Guaranteed Domains of Attraction for Multivariable Luré Systems Via Open Lyapunov Surfaces 1

Abstract In this paper we provide guaranteed stability regions for multivariable Lure systems, Specifically, using the Lure-Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces, It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system

An implicit small gain condition and an upper bound for the real structured singular value

In this paper we develop an upper bound for the real structured singular value that has the form of an implicit small gain theorem. The implicit small gain condition involves a shifted plant whose dynamics depend upon the uncertainty set bound and, unlike prior bounds, does not require frequency-dependent scales or multipliers. Numerical results show that the implicit small gain bound compares favorably with real-/spl mu/ bounds that involve frequency-dependent scales and multipliers.

Real-m bounds based on fixed shapes in the Nyquist plane: parabolas, hyperbolas, cissoids, nephroids, and octomorphs

In this paper we introduce new bounds for the real structured singular value. The approach is based on absolute stability criteria with plant-dependent multipliers that exclude the Nyquist plot from fixed plane curve shapes containing the critical point − + jO. Unlike half-plane and circle-based bounds the critical feature of the fixed curve bounds is their ability to differentiate between the real and imaginary components of the uncertainty. Since the plant-dependent multipliers have the same functional form at all frequencies, the resulting graphical interpretation of the absolute stability criteria are frequency independent in contrast to the frequency-dependent off-axis circles that arise in standard real-μ bounds.

Finite settling time control of the double integrator using a virtual trap-door absorber

Finite settling time control of the double integrator is considered. The approach taken is to design a compensator based on a virtual lossless absorber which is tuned so that, at some predetermined time, the virtual subsystem possesses all of the systems energy. At this time the controller is turned off, and the double integrator remains at rest at the origin. This strategy gives the appearance of instantaneously removing all of the systems energy as if a trap door had been sprung. A practically useful feature of the virtual trap-door absorber is that only position measurement is required. Controller parameters for the virtual trap-door absorber controller are chosen, and the resulting controller is compared to the classical minimal-time and minimal-energy controllers, which require measurements of both position and velocity.

Real-/spl mu/ bounds based on fixed shapes in the Nyquist plane: parabolas, hyperbolas, cissoids, nephroids, and octomorphs

In this paper we introduce new bounds for the real structured singular value. The approach is based on absolute stability criteria with plant-dependent multipliers that exclude the Nyquist plot from fixed plane curve shapes containing the critical point -1+j0. Unlike half-plane and circle-based bounds the critical feature of the fixed curve bounds is their ability to differentiate between the real and imaginary components of the uncertainty. Since the plant-dependent multipliers have the same functional form at all frequencies, the resulting graphical interpretation of the absolute stability criteria are frequency independent in contrast to the frequency-dependent off-axis circles that arise in standard real-/spl mu/ bounds.