Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros

Freitas, Francisco Damasceno; Rommes, Joost; Martins, Nelson

doi:10.1007/978-3-030-95157-3_12

Cited by 1 publication

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 3. The LTI-CTD system (1) is minimal, stable, controllable, and observable; then the eigenvalues of A n have a negative-real part and the controllability Gramian matrix L o and the observability Gramian matrix L c are symmetric, positive definite matrices, satisfying two Lyapunov Equations ( 12) and (13).…”

Section: Mixed Riccati-lyapunov Balanced Truncation (Mrlbt) Algorithmmentioning

confidence: 99%

“…; the Proper Orthogonal Decomposition (POD) [9] group of methods and similar algorithms such as Principal Component Analysis (PCA) [10], etc. ; the group of algorithms on Modal Truncation (MT) [11,12] and improved technique Subspace Accelerated Dominant Pole Algorithm (SADPA) [13]; and the technical group on Gramian balance, represented by balanced truncation (BT) [14], with improved algorithms such as frequencylimited balanced truncation [15], time-limited balanced truncation [16], bounded-real balanced truncation [17], positive-real balanced truncation (PRBT) [18], balanced stochastic truncation [19], linear-quadratic Gaussian balanced truncation [20], H-infinity balanced truncation [21], Hankel-norm approximation [22], etc.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

Dao,

Nguyen,

et al. 2024

Energies

View full text Add to dashboard Cite

This paper proposes a novel algorithm, termed Mixed Riccati–Lyapunov Balanced Truncation (MRLBT), tailored for order reduction of Linear Time-Invariant Continuous-Time Descriptor Systems (LTI-CTD), commonly encountered in electrical and electronic circuit modeling. The MRLBT approach synergistically combines the advantages of balanced truncation (BT) and positive-real balanced truncation (PRBT) techniques while mitigating their limitations. Unlike BT, which preserves stability but not passivity, and PRBT, which retains passivity at the expense of larger reduction errors, MRLBT ensures the preservation of both stability and passivity inherent in the original system. Additionally, MRLBT achieves reduced computational complexity and minimized order reduction errors compared to PRBT. The proposed algorithm transforms the system into an equivalent Mixed Riccati–Lyapunov Balanced form, enabling the construction of a reduced-order model that retains the critical physical properties. Theoretical analysis and proofs are provided, establishing an upper bound on the global order reduction error. The efficacy of MRLBT is demonstrated through a numerical example involving an RLC ladder network, showcasing its superior performance over BT and PRBT in terms of reduced errors in the time and frequency domains.

show abstract

Section: Mixed Riccati-lyapunov Balanced Truncation (Mrlbt) Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

Dao,

Nguyen,

et al. 2024

Energies

View full text Add to dashboard Cite

show abstract

Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros

Cited by 1 publication

References 12 publications

Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

Contact Info

Product

Resources

About