Singular perturbation modelling of large-scale systems with multi-time-scale property

The problem is investigated of singular perturbation modelling, which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large-scale systems. In both continuous- and discrete-time versions, modelling concepts based on structural properties are studied, and computer-oriented algorithms are developed. The results of two-time-scale systems are extended to multi-time-scale cases. Furthermore, in order to verify the validity of these studies, some numerical examples are given.

[1]  W. Miranker,et al.  Multitime Methods for Systems of Difference Equations , 1977 .

[2]  G. Blankenship.  Singularly perturbed difference equations in optimal control problems , 1981 .

[3]  Joe H. Chow,et al.  Time-Scale Modeling of Dynamic Networks with Applications to Power Systems , 1983 .

[4]  Joe H. Chow,et al.  Coherency based decomposition and aggregation , 1982, Autom..

[5]  Magdi S. Mahmoud,et al.  On eigenvalue assignment in discrete systems with fast and slow modes , 1985 .

[6]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[7]  Morishige Kimura,et al.  On the matrix Riccati equation for a singularly perturbed linear discrete control system , 1983 .

[8]  R. Phillips.  Reduced order modelling and control of two-time-scale discrete systems† , 1980 .

[9]  D. Naidu,et al.  A singular perturbation method for discrete control systems , 1980 .

[10]  Hisashi Kando,et al.  Consideration of Eigenvalue Sensitivity for a Reactor System , 1971 .

[11]  William R. Perkins,et al.  Hierarchical Control of Large Scale Systems by Chained Aggregation , 1980 .

[12]  R. B. Kellogg,et al.  Numerical analysis of singular perturbation problems , 1983 .

[13]  Mahmoud E. Sawan,et al.  Nash strategies for discrete-time systems with slow and fast modes , 1983 .

[14]  Bernard Friedland.  Introduction to discrete linear controls , 1977 .

[15]  K. W. Chang.  Singular Perturbations of a General Boundary Value Problem , 1972 .

[16]  D. Siljak,et al.  On structural decomposition and stabilization of large-scale control systems , 1981 .

[17]  Robert E. Skelton,et al.  Model reduction and controller synthesis in the presence of parameter uncertainty , 1986, Autom..

[18]  John R. Beaumont,et al.  Large-Scale Systems: Modeling and Control , 1983 .

[19]  Petar V. Kokotovic,et al.  Singular perturbations and time-scale methods in control theory: Survey 1976-1983 , 1982, Autom..

[20]  G. Stewart.  Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices , 1976 .

[21]  H. Kando,et al.  Initial value problems of singularly perturbed discrete systems via time-scale decomposition , 1983 .

[22]  Mihail M. Konstantinov,et al.  Computational algorithms for linear control systems: a brief survey , 1985 .

[23]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[24]  Joe H. Chow,et al.  Multi-time-scale analysis of a power system , 1979, Autom..

[25]  C. Reinsch,et al.  Balancing a matrix for calculation of eigenvalues and eigenvectors , 1969 .

[26]  Joe H. Chow,et al.  Singular perturbation and iterative separation of time scales , 1980, Autom..

[27]  H. Nicholson.  Dynamic optimisation of a boiler , 1964 .

[28]  Mohammad Mahbubul Hassan,et al.  The simplification of linear discrete-time systems by model-following methods , 1981 .

[29]  D. Teneketzis,et al.  Linear regulator design for stochastic systems by a multiple time-scales method. [hierarchically structured suboptimal controller] , 1977 .

[30]  P. Kokotovic,et al.  Weak connections, time scales, and aggregation of nonlinear systems , 1983 .

[31]  J. Medanic,et al.  Geometric properties and invariant manifolds of the Riccati equation , 1982 .

[32]  P. Sannuti,et al.  Singular perturbation modelling of continuous and discrete physical systems , 1983 .

[33]  H. Khalil,et al.  INFINITE-TIME REGULATORS FOR SINGULARLY PERTURBED DIFFERENCE EQUATIONS. , 1984 .

[34]  Madan G. Singh,et al.  Dynamical Hierarchical Control , 1977 .

[35]  Petar V. Kokotovic,et al.  Singular perturbations and order reduction in control theory - An overview , 1975, at - Automatisierungstechnik.

[36]  W. Hallauer,et al.  A Method of Order Reduction for Structural Dynamics Based on Riccati Iteration , 1981 .

[37]  Jose B. Cruz,et al.  Feedback systems , 1971 .

[38]  Webb Miller,et al.  Software for Roundoff Analysis of Matrix Algorithms , 1980 .

[39]  C. Comstock,et al.  Singular perturbatilons for difference equations , 1976 .

[40]  D. Naidu,et al.  Singular perturbation method for initial-value problems with inputs in discrete control systems , 1981 .

[41]  P. Kokotovic,et al.  Eigenvalue Placement in Two-Time-Scale Systems , 1976 .

[42]  Peter Dorato.  Theoretical developments in discrete-time control , 1983, Autom..

[43]  D. Naidu,et al.  Singularly perturbed boundary-value problems in discrete systems , 1981 .

[44]  L. Litz,et al.  State decomposition for singular perturbation order reduction—A modal approach† , 1981 .

[45]  K. Fernando,et al.  Singular perturbational model reduction of balanced systems , 1982 .