Wei-Min Lu

/spl Hscr//sub /spl infin// control of nonlinear systems: a convex characterization

The nonlinear /spl Hscr//sub /spl infin//-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to /spl Hscr//sub /spl infin//-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. >

/spl Hscr//sub /spl infin// control of nonlinear systems via output feedback: controller parameterization

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

Stabilization of uncertain linear systems: an LFT approach

This paper develops machinery for control of uncertain linear systems described in terms of linear fractional transformations (LFTs) on transform variables and uncertainty blocks with primary focus on stabilization and controller parameterization. This machinery directly generalizes familiar state-space techniques. The notation of Q-stability is defined as a natural type of robust stability, and output feedback stabilizability is characterized in terms of Q-stabilizability and Q-detectability which in turn are related to full information and full control problems. Computation is in terms of convex linear matrix inequalities (LMIs), the controllers have a separation structure, and the parameterization of all stabilizing controllers is characterized as an LFT on a stable, free parameter.

A state-space approach to parameterization of stabilizing controllers for nonlinear systems

A state-space approach to the Youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parameterized output feedback controllers have separation structures. This machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization. >

Robustness analysis and synthesis for nonlinear uncertain systems

A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of nonlinear systems subject to L/sub 2/-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem. As in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the solvability of robustness synthesis problems are represented in terms of NLMIs as well. With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favourable.

Rejection of persistent /spl Lscr//sub /spl infin//-bounded disturbances for nonlinear systems

A nonlinear /spl Lscr//sup 1/-control problem, which deals with the rejection of persistent bounded disturbances for nonlinear systems, is investigated. The concept of invariance plays an important role in the /spl Lscr//sup 1/-performance analysis and synthesis. The main idea is to construct an invariant subset in the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to the subset. The relation between the /spl Lscr//sup 1/-control of a continuous-time system and the l/sup 1/-control of its Euler approximated discrete-time system is established.

H/sub /spl infin// control of nonlinear systems via output feedback: a class of controllers

The standard state space solutions to the H/sub /spl infin// control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H/sub /spl infin// controllers are parametrized as nonlinear fractional transformation on contractive, stable free nonlinear parameters. As in the linear case, the H/sub /spl infin// control problem is solved by its reduction to a state feedback and output injection problems, together with a separation argument. the sufficient conditions for H/sub /spl infin//-control problem to be solved are also derived with this machinery. The solvability for nonlinear H/sub /spl infin// control problem requires positive definite solution to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy and additional coupling condition. An illustrative example, which deals with a passive plant, is given.<<ETX>>

H/sub infinity / control of LFT systems: an LMI approach

The standard H/sub infinity / control problem for linear state-space systems is extended to general LFT systems, which involve a LFT (linear fractional transformation) on a structured free parameter Delta and can be interpreted as structuredly perturbed uncertain systems. Two generalizations of H/sub infinity / performance are considered, referred too as mu -performance and Q-performance with the latter implying the former. Necessary and sufficient conditions for a system to have Q-performance and for the existence of a controller yielding Q-performance can be expressed in terms of structured linear matrix inequalities (LMIs).<<ETX>>

A State-Space Theory of Uncertain Systems

Abstract This paper presents a tutorial summarizing recent work on generalizing standard state-space results such as stability and performance analysis, realization theory, stability and stabilization, and H ∞ optimal control to uncertain systems described by Linear Fractional Transformations (LFTs)

Robustness analysis and synthesis for uncertain nonlinear systems

The stability and performance robustness analysis for a class of uncertain nonlinear systems with bounded structured uncertainties are characterized in terms of various types of nonlinear matrix inequalities (NLMIs). As in the linear case, scalings or multipliers are used to find Lyapunov functions that give sufficient conditions, and the resulting NLMIs yield convex feasibility problem. For these problems, robustness analysis is essentially no harder than stability analysis of the system with no uncertainty. Sufficient conditions for the solvability of related robust synthesis problems are developed in terms of NLMIs as well.<<ETX>>