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

The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems

YALMIP : a toolbox for modeling and optimization in MATLAB

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

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Higher-order sliding modes, differentiation and output-feedback control

We consider nonlinear control systems for which an estimate x/spl circ/ of the system state x is available for feedback. We assume x/spl circ/=x+d/sub m/, where d/sub m/(t) is an unknown locally bounded state measurement disturbance. We present conditions under which we can design a smooth feedback law u=/spl mu/(x/spl circ/) which renders the mapping from d/sub m/ to x globally input/output stable. For any initial condition, such a feedback law will guarantee that no finite escape times occur, that bounded disturbances d/sub m/ produce bounded signals, and that x/spl rarr/0 when d/sub m//spl rarr/0. We show that the class of systems for which such feedback laws exist include systems in strict feedback form. One important application is in the output feedback stabilization problem, where the disturbance d/sub m/ comes from a separately designed observer. >

Global robustness of nonlinear systems to state measurement disturbances

Recent two-time-scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this note the two-time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control. As an illustration, we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations.

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A corrective feedback design for nonlinear systems with fast actuators

Control Lyapunov functions for adaptive nonlinear stabilization

The design of model-reference adaptive control (MRAC) for MIMO linear systems has not yet been achieved, in spite of significant efforts, the completeness and simplicity of its SISO counterpart. One of the main obstacles has been the generalization of the SISO assumption that the sign of the high-frequency gain is known. Here we overcome this obstacle and present a MIMO analog to the well known Lyapunov-based MRAC SISO design. Our algorithm makes use of a new control parametrization derived from a factorization of the high-frequency gain matrix K/sub p/=SDU, where S is symmetric positive definite, D is diagonal, and U is unity upper triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K/sub p/, are assumed to be known.

http://ieeexplore.ieee.org/iel5/7520/20469/00945743.pdf

Lyapunov-based adaptive control of MIMO systems

The concept of integral manifolds is used to create systematically improved reduced-order models of synchronous machines. The approach is illustrated through a detailed example of a single machine connected to an infinite bus. The example shows the advantages of the manifold approach and clarifies several issues regarding such models. The basic objective of the method is to include the effects of more complex models without including the additional differential equations. This is illustrated for the effects of stator transients and damper windings on the swing equation. >

Petar V. Kokotovic

Papers

Global robustness of nonlinear systems to state measurement disturbances

A corrective feedback design for nonlinear systems with fast actuators

Control Lyapunov functions for adaptive nonlinear stabilization

Lyapunov-based adaptive control of MIMO systems

An integral manifold approach to reduced order dynamic modeling of synchronous machines