Exponential feedback passivity and stabilizability of nonlinear systems

Motivated by N. Krasovskii's characterisation of exponential stability, the concept of exponential passivity is introduced. It is shown that to make a nonlinear system with factorisable high-frequency gain matrix exponentially passive via either state or output feedback, exponential minimum phaseness and invertibility conditions are necessary and sufficient. These conditions also guarantee exponential output feedback stabilisability. This result extends previous results concerning linear systems. © 1988 Elsevier Science Ltd. All rights reserved.link_to_subscribed_fulltex

A passification approach to adaptive nonlinear stabilization

In this paper, we unify and extend previously obtained results on adaptive stabilization of nonlinear systems from a passive systems viewpoint. It is shown that, for an interconnected multi-input nonlinear system composed of a chain of feedback strictly passive subsystems, an adaptive controller can be designed to render the closed loop system passive. Further, adaptive regulation is guaranteed if the zero-dynamics equation of each subsystem satisfies an appropriate input/state property. A systematic use of feedback passification in our proposed adaptive control scheme allows a simpler reinterpretation of the backstepping design with tuning functions in Krstić et al. (1992).link_to_subscribed_fulltex

Passivity based damping of power system oscillations

The aim of the paper is to apply the passification and Speed-Gradient methods to the problem of transient stabilization. A controller is proposed and the stability results are established. It is shown that the proposed controller requires only local on-line measurements of relative velocities, i.e., the suggested control law is decentralized and easy to implement. Simulation results prove the ability of the controller to provide transient stabilization of the overall system.link_to_subscribed_fulltex

Adaptive passification of interconnected nonlinear systems

In this paper, we provide some passivity-based tools for adaptive control design of interconnected nonlinear systems. Sufficient conditions are given under which an interconnected nonlinear system with parametric uncertainty is rendered adaptively feedback passive with adaptive regulation.link_to_subscribed_fulltex

Dissipativity of T-periodic linear systems

It is proved that the existence of a positive definite storage function is necessary and sufficient for strict dissipativity of linear systems with periodic coefficients. The connection between strict dissipativity of the system and a nonoscillatory property of an associated Hamiltonian system is established.link_to_subscribed_fulltex

Nonlinear adaptive control of feedback passive systems

An adaptive controller that solves the problem of rendering a system passive is presented for a special class of systems with parametric uncertainty. The proposed control uses techniques of speed-gradient methodology from the Russian literature. Stability results can be given that do not require commonly used assumptions such as linearity in the parameters. Algorithms that render the system strictly passive clarify some already known in the control of mechanical systems.link_to_subscribed_fulltex

Passivity and passification of nonlinear systems

Publications applying the concepts of passivity and dissipativeness to the control of nonlinear systems were reviewed. Criteria for passivity and dissipativeness, properties of passive and dissipative systems, and passification algorithms for nonlinear controlled systems were presented. Applications to stabilization of the nonlinear systems were described. The relation to other approaches was discussed