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

Linear Robust Control

Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the cross-layer interaction from the physical to transport layer in wireless network architectures including cellular, ad-hoc and sensor networks as well as hybrid wireless-wireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Cross-layer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided.

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Resource Allocation and Cross Layer Control in Wireless Networks

All controllers for the general H ∞ control problem: LMI existence conditions and state space formulas

1. Introduction 2. Linear Algebra Review 3. Analysis of First-order Information 4. Second-order Information in Linear Systems 5. Covariance Controllers 6.Covariance Upper Boundary Controllers 7. H-Controllers 8. Model Reduction 9. Unified Perspective 10. Projection Methods 11. Successive Centring Methods 12. A: Linear Algebra Basics 13. B: Calculus of Vectors and Matrices 14. C: Balanced Model Reduction

A unified algebraic approach to linear control design

Consider a given dynamical system, described by ẋ = f(x) (wheref is a nonlinear function) and [x0] a subset ofR. We present an algorithm, based on interval analysis, able to show that there exists a unique equilibrium statex∞ ∈ [x0] which is asymptotically stable. The effective method also provides a set[x] (subset of[x0]) which is included in the attraction domain of x∞.

Ieee transactions on automatic control

In this paper the standard $H_\infty $ control problem using state feedback is considered. Given a linear, time-invariant, finite-dimensional system, this problem consists of finding a static state feedback such that the resulting closed-loop transfer matrix has $H_\infty $ norm smaller than some a priori given upper bound. In addition it is required that the closed-loop system is internally stable. Conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality, reminiscent of the dissipation inequality of singular linear quadratic optimal control. Where the direct feedthrough matrix of the control input is injective, the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic Riccati equation.

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The quadratic matrix inequality in singular H ∞ control with state feedback

De onderwerpen die in dit proefschrift aan de orde komen vallen binnen het kader van de wat men noemt "geometrische aanpak" in de theorie der lineaire systemen. Het grondprobleem is om voor een gegeven ingang/uitgang systeem (het regelsysteem) een nieuw ingang/uitgang systeem te ontwerpen, dat op basis van de uitgangsgrootheid van het regelsysteem (de meting) een ingangsgrootheid voor het regelsysteem genereert zodat het samengestelde systeem bepaalde gewenste kwalitatieve eigenschappen heeft. Een centrale plaats in dit proefschrift wordt ingenomen door het bijna storingsontkoppelingsprobleem. Bij dit probleem gaat het erom een regelaar te ontwerpen zodat het gesloten kring systeem in zekere zin bijna storingsongevoelig wordt. ... Zie: Samenvatting

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Almost invariant subspaces and high gain feedback

In this paper, we investigate in detail the almost disturbance decoupling problem with state feedback. An alternative proof of the sufficiency part of the original result by Willoms (1981) on this problem, requiring the construction of a sequence of feedback matrices, is given. It is shown that one can achieve almost disturbance decoupling by letting some of the closed loop eigenvalues run to infinity according to a spatial arrangement determined by the infinite zero structure. The proofs of our results use the fact that almost controllability subspaces can be approximated by controlled invariant subspaces. Our results on the closed-loop eigenstructure are stated in terms of such approximating sequences. We also prove a generalization of a theorem by Wonham (1979), used in the context of minimal order observer design.

On the assignability of infinite root loci in almost disturbance decoupling

https://pure.rug.nl/ws/files/14408906/1988LinAlgApplTrentelman.pdf

Hendrikus Trentelman

Papers

Ieee transactions on automatic control

The quadratic matrix inequality in singular H ∞ control with state feedback

Almost invariant subspaces and high gain feedback

On the assignability of infinite root loci in almost disturbance decoupling

Almost Invariance and Noninteracting Control: A Frequency-Domain Analysis