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

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

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

Shifts in Redox Formal Potentials Accompanying the Incorporation of Cationic Complexes in Perfluoro Polycarboxylate and Polysulfonate Coatings on Graphite Electrodes

The formal potentials of several redox couples incorporated in coatings of a perfluoropolycarboxylate on graphite electrodes were measured and compared with the formal potentials of the same couples in homogeneous solution. The differences observed agreed with those calculated from the Nernst equation with the independently measured incorporationcoefficients for both halves of the redox couples. The dependences of the shifts in formal potentials on the nature of theincorporating complex ion, the ionic strength, and the temperature were determined and indicated that the incorporationequilibrium is governed by electrostatic and hydrophobic interactions that act in opposite directions. The incorporation ofmost cations examined was driven by large increases in entropy which overcame the usually unfavorable enthalpy changes

Stabilization of Linear Systems with Structured Perturbations

The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations