Analysis and optimization of systems: state and frequency domain approaches for infinite-dimensional systems : proceedings of the 10th international conference, Sophia-Antipolis, France, June 9-12, 1992
Ruth F. Curtain, Alain Benoussan, Jacques-Louis Lions
Springer-Verlag, 1993 - Mathematics - 648 pages
This volume contains the proceedings of the conference "state and Frequency Domain Approaches to Infinite-Dimensional Systems". The aim was to bring together engineers and mathematicians working in the field of linear infinite-dimensional systems who are specialists in one or more of the following categories of mathematical approaches: semigroup approches,p.d.e. approaches, frequency domain approaches and syntheses of state-space and frequency domain approaches. Since these approaches use very different sophisticated mathematical techniques, it is unusual for a scientist to be expert in all of them. On the other hand, there different approaches all purport to address the same control problems for the same classes of linear infinite-dimensional systems. It is therefore important to compare and discuss the advantages and disadvantages of these different mathematical techniques. To help ameliorate the communication gab a series of introductory tutorial lectures were given by specialists in the above-mentioned fields. There were complemented by some key survey papers on more recent research, as well as by papers representing original research in these areas.
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Riccati Equations Arising from Boundary and Point Control Problems
A StaleSpace Approach to the HControl Problems
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admissible algebra analytic applied approach approximation assume assumption asymptotic Banach space beam boundary control bounded closed-loop Co-semigroup compensator computation consider control problems coprime factorizations Corollary Curtain defined Definition denote differential equation dimensional systems distributed parameter systems dynamic eigenvalues equivalent exact controllability example exists exponentially stable feedback systems finite frequency domain given graph topology Hankel operator Hence Hilbert space IEEE Trans imaginary axis impulse response infinite infinite-dimensional systems input input-output Laplace transform Lemma linear systems Logemann Mathematics Moreover multivariable norm observation obtain optimal controller output operator perturbations plant poles Pritchard-Salamon system proof prove rational function rational transfer Re(s respect result Riccati equations robust controller robust stabilization robustness margin satisfies semigroup singular values solution stability radius stabilizable state-space strictly proper subset subspace Suppose Theorem theory time-delay transfer function transfer matrix unbounded unique unstable vector wave equation zero