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Controllability and observability of linear time-varying fractional systems
We consider linear time-varying control problems involving the Caputo fractional derivative. By introducing the controllability Gramian matrix, we...
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Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy...
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Stabilization of spline bases by extension
We present a method to stabilize bases with local supports by means of extension. It generalizes the known approach for tensor product B-splines to a...
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Discrete Periodic Multiresolution Analysis
Periodic multiresolution analyses in the space of periodic complex-valued functions of an integer argument are studied. A characterization of...
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Finite-time model order reduction for K-power bilinear systems via shifted Legendre polynomials
In this paper, we propose a finite-time structure-preserving model reduction method based on the shifted Legendre polynomials for K-power bilinear...
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Automated tight Lyapunov analysis for first-order methods
We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve...
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Characterizations of Functions Associated with Wavelet Analysis
In this chapter, we provide characterizations of various functions associated with wavelet analysis on...
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Analysis of Sparse Recovery Algorithms via the Replica Method
This chapter goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of...
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Doubly autoparallel structure and curvature integrals
On a statistical manifold, we can define autoparallel submanifolds and path integrals of the second fundamental forms ( curvature integrals ) for its...
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Some Remarks on Projective Representations of Compact Groups and Frames
In this paper, we study continuous frames with symmetries from projective representations of compact groups. In particular, we study maximal spanning...
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Exact Controllability for Mean-Field Type Linear Game-Based Control Systems
Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system...
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J-fusion frame operator for Krein spaces
In this article we find a necessary and sufficient condition under which a given collection of subspaces is a J -fusion frame for a Krein space
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Model order reduction for gas and energy networks
To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these...
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Stochastic Parameterization with Dynamic Mode Decomposition
A physical stochastic parameterization is adopted in this work to account for the effects of the unresolved small-scale on the large-scale flow...
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Finite Shift-Invariant Subspaces of Periodic Functions: Characterization, Approximation, and Applications
We discuss approximations of square integrable periodic functions by their projections in finite shift-invariant subspaces and highlight the role of...
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State Linear Systems
In this chapter the system differential equation \(\dot{z}(t) = A z(t) + B u(t)\), \(y(t) = C z(t) + D u(t)\) is introduced. For this state linear...