Matrix Riccati Equations in Control and Systems Theory

property of HRDE.- 5 The periodic Riccati equation.- 5.1 Linear periodic differential equations.- 5.2 Preliminary notation and results for linear periodic systems.- 5.3 Existence results for periodic Hermitian Riccati equations.- 5.4 Positive semi-definite periodic equilibria of PRDE.- 6 Coupled and generalized Riccati equations.- 6.1 Some basic concepts in dynamic games.- 6.2 Non-symmetric Riccati equations in open loop Nash differential games.- 6.3 Discrete-time open loop Nash Riccati equations.- 6.4 Non-symmetric Riccati equations in open loop Stackelberg differential games.- 6.5 Discrete-time open loop Stackelberg equations.- 6.6 Coupled Riccati equations in closed loop Nash differential games.- 6.7 Rational matrix differential equations arising in stochastic control.- 6.8 Rational matrix difference equations arising in stochastic control.- 6.9 Coupled Riccati equations in Markovian jump systems.- 7 Symmetric differential Riccati equations: an operator based approach.- 7.1 Popov triplets: definition and equivalence.- 7.2 Associated objects.- 7.3 Associated operators.- 7.4 Existence of the stabilizing solution.- 7.5 Positivity theory and applications.- 7.6 Differential Riccati inequalities.- 7.7 The signature condition.- 7.8 Differential Riccati theory: A Hamiltonian descriptor operator approach.- 7.8.1 Descriptors and dichotomy.- 7.8.2 Hamiltonian descriptors.- 7.8.3 The stabilizing (anti-stabilizing) solution.- 8 Applications to Robust Control Systems.- 8.1 The Four Block Nehari Problem.- 8.1.1 Problem Statement.- 8.1.2 A characterization of all solutions.- 8.1.3 Main Result.- 8.2 Disturbance Attenuation.- 8.2.1 Problem statement.- 8.2.2 A necessary condition.- 8.2.3 The Disturbance Feedforward Problem.- 8.2.4 The least achievable tolerance of the DF problem.- 9 Non-symmetric Riccati theory and applications.- 9.1 Non-symmetric Riccati theory.- 9.1.1 Basic notions and preliminary results.- 9.1.2 Toeplitz operators and Riccati equations.- 9.2 Application to open loop Nash games.- 9.2.1 Definitions and Hilbert space.- 9.2.2 Unique Nash equilibria.- 9.2.3 The general case.- 9.2.4 If any, then one or infinitely many.- 9.3 Application to open loop Stackelberg games.- 9.3.1 Characterization in Hilbert space.- 9.3.2 Unique Stackelberg equilibria.- 9.3.3 A value function type approach.- A Appendix.- A.1 Basic facts from control theory.- A.2 The implicit function theorem.- References.- List of Figures.