# LMI Properties and Applications in Systems, Stability, and Control Theory

@article{Caverly2019LMIPA, title={LMI Properties and Applications in Systems, Stability, and Control Theory}, author={Ryan James Caverly and James Richard Forbes}, journal={ArXiv}, year={2019}, volume={abs/1903.08599} }

The purpose of this document is to collect and organize properties, tricks, and applications related to linear matrix inequalities (LMIs) from a number of references together in a single document. Proofs of the properties presented in this document are not included when they can be found in the cited references in the interest of brevity. Illustrative examples are included whenever necessary to fully explain a certain property. Multiple equivalent forms of LMIs are often presented to give the…

## 14 Citations

Dissipative Stabilization for Linear Systems with Time-Varying General Distributed Delays

- MathematicsAutom.
- 2020

On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions

- Computer Science2021 American Control Conference (ACC)
- 2021

The imitation learning of linear policies as a constrained optimization problem is formulated, and efficient methods which can be used to enforce stability and robustness constraints during the learning processes are presented.

Linear Matrix Inequality Approaches to Koopman Operator Approximation

- MathematicsArXiv
- 2021

Koopman operator theory [1–4] provides a means to globally represent a nonlinear system as a linear system by transforming its states into an infinite-dimensional space of lifted states. The Koopman…

Fast Zonotope-Tube-based LPV-MPC for Autonomous Vehicles

- Mathematics, EngineeringArXiv
- 2020

An effective online tube-based model predictive control solution for autonomous driving that aims at improving the computational load while ensuring robust stability and performance in fast and disturbed scenarios is presented.

Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees

- Computer ScienceArXiv
- 2021

A polynomial-time algorithm is proposed that guarantees feasibility and constraint satisfaction with high probability under proper conditions of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions.

Distributed $\mathscr{H}_2$ Control for Interconnected Discrete-Time Systems: A Dissipativity-based Approach

- MathematicsArXiv
- 2020

The developed method yields a convex alternative to state-of-the-art methods for distributed discrete-time $\mathscr{H}_2$ control, which are typically not convex or consider unstructured problems.

Stabilizer design for an under-actuated autonomous underwater vehicle in a descriptor model under unknown time delay and uncertainty

- MathematicsTrans. Inst. Meas. Control
- 2022

This paper focuses on autonomous underwater vehicle (AUV) stabilization in the nonlinear descriptor model, as well as some AUV limitations such as model uncertainty, singularity, saturation…

System Norm Regularization Methods for Koopman Operator Approximation

- Computer ScienceArXiv
- 2021

DMD and DMD with control are reformulated as convex optimization problems with linear matrix inequality constraints and hard asymptotic stability constraints and system norm regularizers are considered as methods to improve the numerical conditioning of the approximate Koopman operator.

Feedback Capacity of MIMO Gaussian Channels

- Computer Science, Mathematics2021 IEEE International Symposium on Information Theory (ISIT)
- 2021

This paper solves the problem of finding a computable expression for the feedback capacity of additive channels with colored Gaussian noise in the scenario where the channel has multiple inputs and multiple outputs (MIMO) and the noise process is generated as the output of a state-space model (a hidden Markov model).

H∞-Optimal Tracking Controller for Three-Wheeled Omnidirectional Mobile Robots with Uncertain Dynamics

- Engineering2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2020

The simulation and experimental results show that the proposed LMI-based H∞-optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

## References

SHOWING 1-10 OF 100 REFERENCES

Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations

- MathematicsIEEE Trans. Autom. Control.
- 2001

A new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time, and offers new potentials for problems that cannot be handled using earlier techniques.

Some properties and stability results for sector-bounded LTI systems

- MathematicsProceedings of 1994 33rd IEEE Conference on Decision and Control
- 1994

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector [a, b] in terms of linear matrix inequalities in its state-space realization…

A linear matrix inequality approach to H∞ control

- Mathematics
- 1994

The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach:…

Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems

- Mathematics
- 2002

This paper presents new synthesis procedures for discrete-time linear systems. It is based on a recently developed stability condition which contains as particular cases both the celebrated Lyapunov…

Review of LFTs, LMIs, and mu

- Mathematics[1991] Proceedings of the 30th IEEE Conference on Decision and Control
- 1991

The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu , and linear matrix inequalities (LMIs) in solving LFT problems.…

Least squares stationary optimal control and the algebraic Riccati equation

- Mathematics
- 1971

The optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated. Both the case in which the terminal state is free and that in which the…

Dissipative Systems Analysis and Control: Theory and Applications (2nd Edition)-[Book review; B. Brogliato, R. Lozano, B. Maschke]

- PhysicsIEEE Transactions on Automatic Control
- 2007

The main value of the book is that it us an up-to-date reference of dissipative systems in the framework of many system descriptions, and is a good roadmap to the many contributions on the subject.