Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

Bankmann, Daniel; Mehrmann, Volker; Nesterov, Yurii; Dooren, Paul Van

doi:10.1007/s10013-020-00427-x

Cited by 7 publications

(10 citation statements)

References 20 publications

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“…The software package is written in python 3.6. The code and all the examples can be downloaded under [1].…”

Section: Numerical Resultsmentioning

confidence: 99%

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Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

Bankmann¹,

Mehrmann²,

Nesterov³

et al. 2019

Preprint

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In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous-and discrete-time systems. Numerical methods are derived to solve these equations via steepest ascent and Newton-like methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

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“…The software package is written in python 3.6. The code and all the examples can be downloaded under [1].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Consider a continuous-time system M as in (1) and the transfer function T c as in (2). The transfer function T c (s) is called positive real if the matrix-valued rational function…”

Section: Positive-realness and Passivity Continuous-timementioning

confidence: 99%

Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

Bankmann¹,

Mehrmann²,

Nesterov³

et al. 2019

Preprint

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“…We have that a regular strangeness-free pHDAE system is passive, but in general not necessarily strictly passive, since W in (4.8) is only assumed positive semi-definite. To obtain strict passivity, it is necessary to consider the system in the formulation with feedthrough term and similarly we can analyze how to obtain robust representations as is done for pHODE systems in [20,24,161]. For pHDAE systems, this is again an active research topic.…”

Section: Control Methods For Phdae Systemsmentioning

confidence: 99%

Control of port-Hamiltonian differential-algebraic systems and applications

Mehrmann¹,

Unger²

2022

Preprint

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The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving interconnection, congruence transformations, and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity, and numerical methods to check these properties.After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analyzed, time-discretization, and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.The properties of port-Hamiltonian descriptor systems and their use in modeling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

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“…We note that solutions to the Lyapunov inequality (2.6) are typically not unique, and one can use this freedom to determine solutions that optimize certain robustness measures like the distance to instability, see e.g. [7,11,20].…”

Section: Example 4 Consider the Matrix In Example 1 In Agreement With...mentioning

confidence: 99%

Hypocoercivity and hypocontractivity concepts for linear dynamical systems

Achleitner¹,

Arnold²,

Mehrmann³

2022

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For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability and (semi-)dissipativity respectively (semi-)contractivity. On the basis of these results, the short time decay-behavior of the solutions of linear continuous-time and discrete-time systems is characterized.

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Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

Cited by 7 publications

References 20 publications

Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis

Control of port-Hamiltonian differential-algebraic systems and applications

Hypocoercivity and hypocontractivity concepts for linear dynamical systems

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