Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach

The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated

Teacher Contract Non-Renewal in the Rocky Mountains

Success for students in the 21st century increasingly relies on competencies and proficiencies typically available on]y through formal educational processes. Researchers have noted the paramount importance of quality teaching as the important criterion for student success (Haycock, 1998; Marzano, 2003). Recent reforms have increased the expectation that school principals energetically address teacher evaluations and subsequently remove ineffective teachers. These recent reforms tend to have common priorities, including emphasizing high quality teaching, evaluating teachers for merit pay purposes, and linking evaluation to student performance with an emphasis on the removal of ineffective teachers from the classroom

Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties

Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties

Quadratic stability with real and complex perturbations

It is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear, fractional, unstructured perturbations does not hold when the perturbations are block structured. For a limited class of problems, quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms, and hence appropriate synthesis techniques, coupled with diagonal constant scalings, can be used to design quadratically stable systems

Review of LFTs, LMIs, and μ

The purpose of this paper is to present a tutorial overview of Linear Fractional Transformations (LFT) and the role of the Structured Singular Value, μ, and Linear Matrix Inequalities (LMI) in solving LFT problems

Structured singular value with repeated scalar blocks

The structured singular value, μ, is an important linear algebra tool to study a class of matrix perturbation problems, [Doy]. It is useful for analyzing the robustness of stability and performance of dynamical systems [DoyWS]. This paper studies uncertainty structures involving repeated scalar parameters in more detail than in [Doy]. In [DoyP], it was shown that the frequency domain μ tests of [DoyWS] can conceptually be reduced to a single constant matrix μ test, but the uncertainty structure must be augmented with a large repeated scalar block. This paper studies the properties of μ and the upper bound with these types of uncertainty blocks, and compares the frequency domain vs. state space μ based tests, assuming that the upper bound is what can be reliably computed

Quadratic stability with real and complex perturbations

It is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear, fractional, unstructured perturbations does not hold when the perturbations are block structured. For a limited class of problems, quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms, and hence appropriate synthesis techniques, coupled with diagonal constant scalings, can be used to design quadratically stable systems

A General Statement of Structured Singular Value Concepts

Some key concepts of strucred singular value theory for the stability and performance-robustness analysis of linear time-invariant multivariable systems are stated. Using a set-invariance principle, the theory is then generalized to allow for nonlinear and/or time-varying nominal systems and uncertainties. The general theory is then re-specialized to the case of nominally linear time-invariant systems subject to L2-induced-norm bounded uncertainties

Design examples using µ-synthesis: Space shuttle lateral axis FCS during reentry

This paper studies the application of Structured Singular Values (SSV or µ) for analysis and synthesis of the Space Shuttle lateral axis flight control system (FCS) during reentry. While this is a fairly standard FCS problem in most respects, the aircraft model is highly uncertain due to the poorly known aerodynamic characteristics (e.g. aero coefficients). Comparisons are made of the conventional FCS with alternatives based on H∞ optimal control and µ-synthesis. The problem as formulated is particularly interesting and challenging because the uncertainty is large and highly structured

Development of Advanced Control Design Software for Researchers and Engineers

This paper provides a brief description of The μ Analysis and Synthesis Toolbox (μ-Tools), an advanced control design toolbox to be used in conjunction with MATLAB