Optimal and robust control : advanced topics with MATLAB́

Content: Modelling of uncertain systems and the robust control problem Uncertainty and robust control The essential chronology of major findings into robust control  Fundamentals of stability Lyapunov criteria Positive definite matrices Lyapunov theory for linear time-invariant systems Lyapunov equations Stability with uncertainty Exercises  Kalman canonical decomposition Introduction Controllability canonical partitioning Observability canonical partitioning General partitioning Remarks on Kalman decomposition Exercises  Singular value decomposition Singular values of a matrix Spectral norm and condition number of a matrix Exercises  Open-loop balanced realization Controllability and observability gramians Principal component analysis Principal component analysis applied to linear systems State transformations of gramians Singular values of linear time-invariant systems Computing the open-loop balanced realization Balanced realization for discrete-time linear systems Exercises  Reduced order models Reduced order models based on the open-loop balanced realization Reduced order model exercises Exercises  Symmetrical systems Reduced order models for SISO systems Properties of symmetrical systems The cross-gramian matrix Relations between W2c , W2o and Wco Open-loop parameterization Relation between the Cauchy index and the Hankel matrix Singular values for a FIR filter Singular values of all-pass systems Exercises  Linear quadratic optimal control LQR optimal control Hamiltonian matrices Resolving the Riccati equation by Hamiltonian matrix The Control Algebraic Riccati Equation Optimal control for SISO systems Linear quadratic regulator with cross-weighted cost Finite-horizon linear quadratic regulator Optimal control for discrete-time linear systems Exercises  Closed-loop balanced realization Filtering Algebraic Riccati Equation Computing the closed-loop balanced realization Procedure for closed-loop balanced realization Reduced order models based on closed-loop balanced realization Closed-loop balanced realization for symmetrical systems Exercises  Passive and bounded-real systems Passive systems Circuit implementation of positive-real systems Bounded-real systems Relationship between passive and bounded-real systems Exercises  H  linear control Introduction Solution of the H  linear control problem The H  linear control and the uncertainty problem Exercises  Linear Matrix Inequalities for optimal and robust control Definition and properties of LMI LMI problems Formulation of control problems in LMI terms Solving a LMI problem LMI problem for simultaneous stabilizability Solving algebraic Riccati equations through LMI Computation of gramians through LMI Computation of the Hankel norm through LMI H  control Multiobjective control Exercises  The class of stabilizing controllers Parameterization of stabilizing controllers for stable processes Parameterization of stabilizing controllers for unstable processes Parameterization of stable controllers Simultaneous stabilizability of two systems Coprime factorizations for MIMO systems and unitary factorization Parameterization in presence of uncertainty Exercises  Recommended essential references  Appendix A. Norms  Appendix B. Algebraic Riccati Equations  Index