Some notes on port-Hamiltonian systems on Banach spaces

We consider port-Hamiltonian systems from a functional analytic perspective. Dirac structures and Hamiltonians on Banach spaces are introduced, and an energy balance is proven. Further, we consider port-Hamiltonian systems on Banach manifolds, and we present some physical examples that fit into the presented theory

A pseudo-resolvent approach to abstract differential-algebraic equations

We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a~pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply our results to some examples such as distributed circuit elements, and a system obtained by heat-wave coupling

Funnel control for boundary control systems

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop system is proved by using nonlinear operator theory. We apply our results to both hyperbolic and parabolic equations.Comment: 26 pages, thoroughly revised version. The system class has been generalized considerably. Added general example class of parabolic problem

Analysis of an iteration method for the algebraic Riccati equation

We consider a recently published method for solving algebraic Riccati equations. We present a new perspective on this method in terms of the underlying linear-quadratic optimal control problem: we prove that the matrix obtained by this method expresses the optimal cost for a projected optimal control problem. The projection is determined by the so-called “shift parameters” of the method. Our representation in terms of the optimal control problem gives rise to a simple and very general convergence analysis

Operator Splitting Based Dynamic Iteration for Linear Port-Hamiltonian Systems

A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no stability conditions are required. The developed iteration scheme is even new for linear port-Hamiltonian systems. The obtained algorithm is applied to multibody systems and electrical networks.Comment: 29 pages, 6 figure

A lower bound for the balanced truncation error for MIMO systems

We show that for a class of systems which includes state space symmetric systems, the balanced truncation error is bounded from below by twice the sum of the tail of the Hankel singular values (including multiplicities) divided by the dimension of the input space

Positive real and bounded real balancing for model reduction of descriptor systems

We present an extension of the positive real and bounded real balanced truncation model reduction methods to large-scale descriptor systems. These methods are based on balancing the solutions of the projected Lur'e matrix equations. Important properties of these methods are that, respectively, passivity and contractivity are preserved in the reduced-order models and that there exist approximation error bounds. We also discuss the numerical solution of the projected Lur'e equations. Numerical examples are given

Frequency Domain Methods and Decoupling of Linear Constant Coefficient Infinite Dimensional Differential Algebraic Systems

We discuss the analysis of constant coefficient linear differential algebraic equations $E\dot{x}(t)=Ax(t)+q(t)$ on infinite dimensional Hilbert spaces. We give solvability criteria of these systems which are mainly based on Laplace transformation. Furthermore, we investigate decoupling of these systems, motivated by the decoupling of finite dimensional differential algebraic systems by the Kronecker normal form. Applications are given by the analysis of mixed systems of ordinary differential, partial differential and differential algebraic equations