Lyapunov Matrix Equation in System Stability and Control

Abstract

Part 1 Introduction: stability of linear systems variance of linear stochastic systems quadratic performance measure book organization. Part 2 Continuous algebraic Lyapunov equation: explicit solutions solution sounds numerical solutions. Part 3 Discrete algebraic Lyapunov equation: explicit solutions bounds of solution's attributes numerical solutions. Part 4 Differential and difference Lyapunov equation: explicit solutions bounds of solution's attributes numerical solutions singularly perturbed and weakly coupled systems coupled differential equations. Part 5 Algebraic Lyapunov equation with small parameters: singularly perturbed continuous Lyapunov equation weakly coupled continuous Lyapunov equation singularly perturbed discrete systems recursive methods for weakly coupled discrete systems. Part 6 Robustness and sensitivity of the Lyapunov equation: stability robustness sensitivity of algebraic Lyapunov equation. Part 7 Iterative methods and parallel algorithms: Smith's algorithm ADI iterative method SOR iterative method parallel algorithms parallel algorithms for coupled Lyapunov equations. Part 8 Lyapunov iterations: Kleinman algorithm for Riccati equation Lyapunov iterations for jump linear systems Lyapunov iterations for Nash differential games Lyapunov iterations for output feedback control. Part 9 Concluding remarks: Sylvester equations related topics applications. Appendix: matrix inequalities.