Titlebook: Mathematical Control Theory; An Introduction Jerzy Zabczyk Textbook 2020Latest edition Springer Nature Switzerland AG 2020 Mathematical Con

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Controllability their adjoint operators. The abstract results lead to specific descriptions of approximately controllable and exactly controllable systems which are applicable to parabolic and hyperbolic equations. Formulae for controls which transfer one state to another are given as well.

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Stability and stabilizabilityIn this chapter stable linear systems are characterized in terms of associated characteristic polynomials and Lyapunov equations. A proof of the Routh theorem on stable polynomials is given as well as a complete description of completely stabilizable systems. Luenberger’s observer is introduced and used to illustrate the concept of detectability.

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Realization theoryThis chapter is devoted to the input–output map generated by a linear control system. The input–output map is characterized in terms of the impulse response function and the transfer function.

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Stability and stabilizabilityThree types of stability and stabilizability are studied: exponential, asymptotic and Lyapunov. Discussions are based on linearization and Lyapunov’s function approaches. When analysing a relationship between controllability and stabilizability topological methods are used.

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Dynamic programming for impulse control   The dynamic programming approach is applied to impulse control problems. The existence of optimal impulse strategy is deduced from general results on fixed points for monotonic and concave transformations.