Svetoslav Savov

New upper estimates for the solution of the continuous algebraic Lyapunov equation

A new result for bounding the summations for solution eigenvalues of the algebraic Lyapunov equation is presented. This makes possible to generate the best known upper scalar solution estimates.

Robust Stability Analysis for a Perturbed Single-Area Power System Model

Abstract This research work investigates the derivation of a fixed upper matrix bound for the solution of one class of parameter-dependent Continuous Algebraic Lyapunov Equations (CALE). It is supposed that the nominal coefficient matrix is subjected to real structured parametric uncertainty belonging to a convex set. The bound is used to analyze the robust stability and the performance behavior of a load-frequency control system for a single area power system model. By means of the bound one can easily estimate the distance from instability of the uncertain system and the linear quadratic performance index associated with it. The applicability of the obtained results is illustrated by an example.

Noniterative Improvement of Trace Bounds for the Lyapunov Equation Solution

The improvement problem for available lower and upper trace bounds for the solution of the continuous-time Lyapunov equation (LE) is investigated. It is shown how an arbitrary positive (semi)-definite lower matrix solution bound can be used to get always tighter trace estimates.

Experimental Study of Lyapunov Equation Solution Bounds for Power Systems Models

Abstract This research work investigates the applicability of some lower and upper, matrix and scalar bounds for the solution of the Continuous Algebraic Lyapunov Equation (CALE), when the coefficient matrices are the state matrices of real data models. The bounds are illustrated for two different models describing the dynamic behavior of power systems - a two-area power system and an interconnected power system. Some important conclusions referring to the accuracy of the respective estimates are made, as well.

Technical Note: DLSDP: The decentralised linear systems design package

Abstract When control theory is applied to solve problems of large scale systems an important feature called decentralisation often arises. Due to the non-classical information pattern, it is in general impossible to exploit classical techniques for control design. This paper describes several decentralised control design methods and a FORTRAN package DLSDP based on them. The organisation of the paper is as follows. Section 1 is an introduction to the decentralised control problem. Classes of systems under control considered in the paper are presented in section 2. Main problems closely related with decentralised control design are pointed out as well. Methods for design of stabilising control for systems with and without pure time-delays, optimal control and robust under structural perturbations control are described and discussed in section 3. The FORTRAN package features and software capabilities are discussed in section 4. The subroutines and their algorithms are described in detail. A numerical example, illustrating the solution of design problems by DLSDP, is given in section 5.