Linear Systems Theory, Second Edition

"Linear Systems Theory", second edition is a comprehensive text that presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more. Intended to be more mainstream than its predecessor, this revision does maintains the rigorous mathematical approach of the first edition. Many of the longer case studies will be replaced with numerical examples drawn mainly from electrical and mechanical engineering applications. Expanded explanations of both linear and nonlinear systems and new problem sets at the end of each chapter are included in the Second Edition. The chapter on neural networks has been expanded to include the many advances that have occurred in that system since the publication of the previous edition.
-- Presents new examples and problems featuring EE/ME applications
-- Is self-contained for reference use
-- Suitable for cross-disciplined courses in systems theory
-- Focuses on computer-oriented techniques

This second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more.Linear Systems Theory discusses:Nonlinear and linear systems in the state space form and through the transfer function methodStability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stabilityControllabilityObservabilityCanonical formsSystem realizations and minimal realizations, including state space approach and transfer function realizationsSystem designKalman filtersNonnegative systemsAdaptive controlNeural networksThe book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences.What's New in the Second Edition?Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studiesExpanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapterIllustrative examples in all the chaptersAn introduction and analysis of new stability conceptsAn expanded chapter on neural networks, analyzing advances that have occurred in that field since the first editionAlthough more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material.Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.

IntroductionMathematical BackgroundIntroductionMetric Spaces and Contraction Mapping TheoryVectors and MatricesMathematics of Dynamic ProcessesSolution of Ordinary Differential EquationsSolution of Difference EquationsCharacterization of SystemsThe Concept of Dynamic SystemsEquilibrium and LinearizationContinuous Linear SystemsDiscrete SystemsApplicationsStability AnalysisThe Elements of the Lyapunov Stability TheoryBIBO StabilityApplicationsControllabilityContinuous SystemsDiscrete SystemsApplicationsObservabilityContinuous SystemsDiscrete SystemsDualityApplicationsCanonical FormsDiagonal and Jordan FormsControllability Canonical FormsObservability Canonical FormsApplicationsRealizationRealizability of Weighting PatternsRealizability of Transfer FunctionsApplicationsEstimation and DesignThe Eigenvalue Placement TheoremObserversReduced-Order ObserversThe Eigenvalue Separation TheoremApplicationsAdvanced TopicsNonnegative SystemsThe Kalman-Bucy FilterAdaptive Control SystemsNeural NetworksBibliographyIndex