This comprehensive text is unique in providing a generalization of the algebraic Riccati theory for the indefinite sign and singular cases from the perspective of the Popov function approach. The theory embodies a systematic presentation from the time domain, frequency domain and state-space standpoints. The whole development is oriented towards applications in robust systems theory.

• Extension of the celebrated Popov positivity theory to the game theoretic case
• Characterizations of the solutions to the Riccati equation in terms of the input-output operator, transfer function matrix and transmission matrix pencil, all associated with the underlying Hamiltonian system
• Comprehensive treatment of both continuous and discrete time cases
• A signature condition based approach which unifies the solutions to various mathematical problems from robust control theory, including the maxmin, Nehari, H2, H??? control and robust stabilization problems

Graduate students in control engineering and those working on the mathematics of systems and control theory will find this book essential reading. For researchers, this is an indispensable work, when seeking ever more robust control laws which take uncertainties into account.

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