Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

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Supervisory control of a class of discrete event processes

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Mathematical Control Theory: Deterministic Finite Dimensional Systems

A long-run equilibrium theory of turnover is presented and is shown to explain the important regularities that have been observed by empirical investigators. A worker's productivity in a particular job is not known ex ante and becomes known more precisely as the worker's job tenure increases. Turnover is generated by the existence of a nondegenerate distribution of the worker's productivity across different. The nondegeneracy is caused by the assumed variation in the quality of the worker-employer match.

Job Matching and the Theory of Turnover

A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

The control of discrete event systems

It can be shown that the problem of reliable transmission of data over an unreliable communication channel can be restated as a decentralized control problem of discrete-event systems. Necessary and sufficient conditions for the existence of solutions to such decentralized supervisory control problems have been found. These conditions are used to verify the correctness of a protocol for the data transmission problem. In particular, it is demonstrated that the authors' method provides a systematic check on whether the protocol satisfies the required safety property, as opposed to relying on finding, ad hoc, circumstances under which the protocol fails. >

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Protocol verification using discrete-event systems

In previous work the authors proposed a distributed diagnosis approach consisting of two phases--preliminary diagnosis in each local diagnoser and inter-diagnoser communication. The objective of communication is to achieve either global or local consistency among local diagnoses, where global consistency is captured by the equilibrium concept of supremal global support. To achieve this equilibrium, an algorithm called Computational Procedure for Global Consistency (CPGC) was proposed. But it turns out that CPGC has high time complexity and weak scalability. To rectify these shortcomings, we propose a hierarchical computational procedure. A further advantage of this procedure is demonstrated, based on multiresolutional diagnosis. With the latter, fault detection is conducted at each hierarchical level, so that computation can be confined to those modules likely to possess faults, while fault-free modules are safely disregarded. A simplified industrial example is provided in illustration.

Hierarchical Fault Diagnosis for Discrete-Event Systems under Global Consistency

Paper: Geometric state-space theory in linear multivariable control: A status report

The design of reduced supervisors, suboptimal but easier to compute, is placed in a general perspective. From this vantage point, we consider a timed discrete-event system, and compute a reduced supervisor based on an abstraction of the plant model in which time is measured with a slower clock. Such a model is simpler than the original, but has richer untimed behavior. Thus, a time-independent specification met by the closed-loop reduced system is also met by the original system when controlled by the same supervisor. The idea is illustrated with a simple example.

Reduced supervisors for timed discrete-event systems

Fixed-time regulator problem with time invariant feedback control and unspecified-time regulator problem with bounded control

W. M. Wonham

Papers

Protocol verification using discrete-event systems

Hierarchical Fault Diagnosis for Discrete-Event Systems under Global Consistency

Paper: Geometric state-space theory in linear multivariable control: A status report

Reduced supervisors for timed discrete-event systems

On a problem of letov in optimal control