Exponential stability of controllers using reduced order actuator and system models with residual mode filters

2000 ◽  
Author(s):  
C.W. Hindman ◽  
M.J. Balas ◽  
M. Lesoinne
Keyword(s):  
Exponential Stability ◽  
Reduced Order ◽  
System Models

scholarly journals On Guaranteed Global Exponential Stability Of Polynomial Singularly Perturbed Control Systems

2006 ◽  
Vol 1 (4) ◽  
pp. 21 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Integral Manifold ◽  
Singularly Perturbed ◽  
Linear Matrix ◽  
Singularly Perturbed Systems ◽  
Closed Loop System ◽  
Reduced Order ◽  
Perturbed Systems ◽  
The Stability

The problem of global exponential stability for a class of nonlinear singularly perturbed systems is examined in this paper. The stability analysis is based on the use of basic results of integral manifold of nonlinear singularly perturbed systems, the composite Lyapunov method and the notations and properties of Tensoriel algebra. Some of the derived results are presented as linear matrix inequalities (LMIs) feasibility tests. Moreover, we pointed out that if the global exponential stability of the reduced order subsystem is established this is equivalent to guarantee the global exponential stability of the original high order closed loop system. An upper bound e1 of the small parameter e , can also be determined up to which established stability conditions via LMI’s are maintained verified. A numerical example is given to illustrate the proposed approach.

scholarly journals SVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models

2021 ◽  
Author(s):  
Mahtab Uddin ◽  
M. Monir Uddin ◽  
M. A. Hakim Khan ◽  
M. Tanzim Hossain
Keyword(s):  
Power System ◽  
Riccati Equations ◽  
Descriptor Systems ◽  
Low Rank ◽  
Reduced Order Models ◽  
Reduced Order ◽  
System Models ◽  
Reduced Order Modelling ◽  
Feedback Matrix ◽  
Finite Solution

We propose an efficient sparsity-preserving reduced-order modelling approach for index-1 descriptor systems extracted from large-scale power system models through two-sided projection techniques. The projectors are configured by utilizing Gramian based singular value decomposition (SVD) and Krylov subspace-based reduced-order modelling. The left projector is attained from the observability Gramian of the system by the low-rank alternating direction implicit (LR-ADI) technique and the right projector is attained by the iterative rational Krylov algorithm (IRKA). The classical LR-ADI technique is not suitable for solving Riccati equations and it demands high computation time for convergence. Besides, in most of the cases, reduced-order models achieved by the basic IRKA are not stable and the Riccati equations connected to them have no finite solution. Moreover, the conventional LR-ADI and IRKA approach not preserves the sparse form of the index-1 descriptor systems, which is an essential requirement for feasible simulations. To overcome those drawbacks, the fitting of LR-ADI and IRKA based projectors from left and right sides, respectively, desired reduced-order systems attained. So that, finite solution of low-rank Riccati equations, and corresponding feedback matrix can be executed. Using the mechanism of inverse projection, the Riccati-based optimal feedback matrix can be computed to stabilize the unstable power system models. The proposed approach will maintain minimized ℌ2 -norm of the error system for reduced-order models of the target models.

Use of a Reduced Order Model (ROM) to Simulate SOFC Performance in System Models

2017 ◽  
Vol 78 (1) ◽  
pp. 2595-2605 ◽  
Author(s):  
Brian J Koeppel ◽  
Canhai Lai ◽  
Arun K.S. Iyengar ◽  
Zhijie Xu ◽  
Chao Wang ◽  
...  
Keyword(s):  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
System Models

scholarly journals Reduced Order vs. Discretized Lumped System Models with Absolute and Relative States for Continuum Manipulators

2019 ◽  
Author(s):  
Seyedmohammadhadi Sadati ◽  
Ali Shiva ◽  
Seyedeh Elnaz Naghibi ◽  
Caleb Rucker ◽  
Ludovic Renson ◽  
...  
Keyword(s):  
Reduced Order ◽  
System Models ◽  
Continuum Manipulators ◽  
Relative States
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