Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems

A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established

Periodic Filters with a Three-Mirror Gire-Tournois Resonator in a Michelson Interferometer

A periodic optical filter based on a Michelson interferometer with a three-mirror Gire-Tournois resonator in one of the two arms is analyzed. We derive the general condition for the occurrence of flattop spectra. The results show that flattop spectra can be obtained by suitably choosing the reflective coefficients of individual mirrors

Design Optimization of Flattop Interleaver and Its Dispersion Compensation

The objective of this paper is to present a general strategy for design optimization of flattop interleavers, and dispersion compensation for the interleavers, in order to achieve superior optical performance. The interleaver is formed by two multi-cavity Gire-Tournois etalons (MC-GTE) in a Michelson Interferometer (MI). An interleaver that has m cavities in one etalon and n cavities in the other is called an mn-GTE interleaver. Our optimization strategy exploits the general flattop condition and the technique of ripple equalization. Any mn-GTE interleaver may be optimized. The spectral performance can be greatly improved by the optimization process. As an illustration, we present a comprehensive analysis for a 11-GTE and a 21-GTE interleaver. The analytical expressions for flattop conditions, peak and trough positions are derived for optimization. The optimal performance of the interleavers can be controlled by the reflection coefficients and the parameters m and n. To achieve low-dispersion mn-GTE flattop interleavers, we propose to use one additional MC-GTE as a dispersion compensator to compensate for the chromatic dispersion. The analytical expressions of group delays and chromatic dispersions for an MC-GTE interleaver are derived. The optimization strategy of dispersion-ripple equalization is explained. The results show that the dispersion performance can be tailored by changing the reflection coefficients of the MC-GTE, and the dispersion and bandwidth can be enhanced by increasing the number of cavities of the MC-GTE

Bankruptcy risk and the performance of tradable permit markets

We study the impacts of bankruptcy risk on markets for tradable environmental and natural resource permits. We show that bankruptcy risk in a competitive market for tradable permits causes an inefficient distribution of these permits among firms. Moreover, the equilibrium distribution of permits is dependent of the initial distribution of permits. Thus, the main reasons for implementing markets for environmental and natural resource rights do not hold when some firms are financially insecure.Limited liability

ℋ∞ control of nonlinear systems via output feedback: controller parameterization

The standard state space solutions to the ℋ∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of local nonlinear (output feedback) ℋ∞ controllers are parameterized as nonlinear fractional transformations on contractive, stable nonlinear parameters. As in the linear case, the ℋ∞ control problem is solved by its reduction to state feedback and output estimation problems, together with a separation argument. Sufficient conditions for ℋ∞-control problem to be locally solved are also derived with this machinery

H∞ control of nonlinear systems: a convex characterization

The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed

H∞ Control of Nonlinear Systems: A Class of Controllers

The standard state space solutions to the H∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H∞-controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the H∞ control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for H∞ control problem to be solved are also derived with this machinery. The solvability for nonlinear H∞-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end