1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

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Essentials of Robust Control

Time-delay systems: an overview of some recent advances and open problems

On optimal e ∞ to e ∞ filtering

This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers. The design objectives can be a mix of H/sub /spl infin// performance, H/sub 2/ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example.

/pdf/multiobjective-output-feedback-control-via-lmi-optimization-8cihrh828q.pdf

Multiobjective output-feedback control via LMI optimization

Survey paper: Set invariance in control

The problems of filtering and smoothing are considered for linear systems in an H/sup infinity / setting, i.e. the plant and measurement noises have bounded energies (are in L/sub 2/), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered; the initial condition is assumed known in one case, while in the other the initial condition is not known but the initial condition, the plant, and measurement noise are in some weighted ball of R/sup n/XL/sub 2/. Finite-horizon and infinite-horizon cases are considered. Necessary and sufficient conditions are presented for the existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, and algorithms that result in performance within the bounds are developed. In case of smoothers, the optimal smoother is also presented. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which both linear time-varying and time-invariant systems can be considered with equal ease. (In the smoothing problem, for linear time-varying systems, one considers only the finite-horizon case). >

Filtering and smoothing in an H/sup infinity / setting

In this paper we offer a novel approach to control-oriented model validation problems. The problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input-output data. Our approach directly uses time-domain input-output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems. In special cases, we give analytical solutions to these problems. >

A time-domain approach to model validation

In this paper we take a new approach to the problem of peak-to-peak gain minimization (the L1 or induced L∞ problem). This is done in an effort to circumvent the complexity problems of other approaches. Instead of minimizing the induced L∞ norm, we minimize the * -norm, the best upper bound on the induced L∞ norm obtainable by bounding the reachable set with inescapable ellipsoids. Controller and filter synthesis for * -norm minimization reduces to minimizing a continuous function of a single real variable. This function can be evaluated, in the most complicated case, by solving a Riccati equation followed by an LMI eigenvalue problem. We contend that synthesis is practical now, but a key computational question-is the function to be minimized convex?—remains open. The filters and controllers that result from this approach are at most the same order as the plant, as in the case of LQG and H∞ design.

A linear matrix inequality approach to peak‐to‐peak gain minimization

H/sub infinity / control and filtering problems for sampled-data systems are studied. Necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified H/sub infinity / performance bound. When these conditions hold, explicit formulas for a controller and a filter satisfying the H/sub infinity / performance bound are also given. >

H/sub infinity / control and filtering for sampled-data systems

In this paper we offer a novel approach to control-oriented model validation problems. This approach differs from other available techniques in that it directly uses time-domain input output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally non-differentiable) convex feasibility programming problems.

K.M. Nagpal

Papers

Filtering and smoothing in an H/sup infinity / setting

A time-domain approach to model validation

A linear matrix inequality approach to peak‐to‐peak gain minimization

H/sub infinity / control and filtering for sampled-data systems

A Time-Domain Approach to Model Validation