Matrix Differential Calculus with Applications in Statistics and Econometrics

The note considers the L/sub 2/-disturbance attenuation of multimachine power systems via dissipative pseudo-Hamiltonian realization of the systems. First, the note expresses multimachine systems as a dissipative Hamiltonian system. Then, the note investigates the energy-based control design of L/sub 2/-disturbance attenuation of multimachine power systems and proposes a decentralized simple control strategy. Simulations on a six-machine system show that the achieved L/sub 2/-disturbance attenuation control strategy is very effective.

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Dissipative Hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems

This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. For switched systems with persistent dwell-time, the output persistent excitation condition is guaranteed to hold under a zero-state observability condition. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria. Interestingly, as opposed to previous work, the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin. The robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria. A novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots.

Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots

Brief Generalized Hamiltonian realization of time-invariant nonlinear systems

This note considers finite time stabilization of uncertain chained form systems. The objective is to design a nonsmooth state feedback law such that the controlled chained form system is both Lyapunov stable and finite-time convergent within any given settling time. We propose a novel switching control strategy with help of homogeneity, time-rescaling, and Lyapunov-based method. Also, the simulation results show the effectiveness of the proposed control design approach.

Stabilization of uncertain chained form systems within finite settling time

This paper deals with chained form systems with strongly nonlinear disturbances and drift terms. The objective is to design robust nonlinear output feedback laws such that the closed-loop systems are globally exponentially stable. The systematic strategy combines the input-state-scaling technique with the so-called backstepping procedure. A dynamic output feedback controller for general case of uncertain chained system is developed with a filter of observer gain. Furthermore, two special cases are considered which do not use the observer gain filter. In particular, a switching control strategy is employed to get around the smooth stabilization issue (difficulty) associated with nonholonomic systems when the initial state of system is known.

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Output feedback exponential stabilization of uncertain chained systems

In this paper, a multi-machine power system is first represented as the generalized Hamiltonian control system with dissipation. Then, a decentralized saturated steam valving and excitation controller, which is statically measurable, is proposed based on the Hamiltonian function method. Finally, an example of three-machine power system is discussed in detail.

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Nonlinear decentralized saturated controller design for power systems

This note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances. The objective is to design a robust nonlinear state feedback law such that the closed-loop system is globally Kexponentially stable. We propose a novel switching control strategy involving the use of input/state scaling and integrator backstepping. The new features of our controllers include the ability to achieve Lyapunov stability, exponential convergence, and robustness to a set of uncertain drift terms.

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A switching algorithm for global exponential stabilization of uncertain chained systems

Energy-Based Stabilization of Forced Hamiltonian Systems with its Application to Power Systems

The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the o-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, called N -group, and its Lie algebra, called N -algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.

Zairong Xi

Papers

Output feedback exponential stabilization of uncertain chained systems

Nonlinear decentralized saturated controller design for power systems

A switching algorithm for global exponential stabilization of uncertain chained systems

Energy-Based Stabilization of Forced Hamiltonian Systems with its Application to Power Systems

Geometric structure of generalized controlled Hamiltonian systems and its application