Linear Systems Theory

Szidarovszky, Ferenc

Presenting important tools of linear systems, this volume explores differential and difference equations, Laplace and Z transforms, and more. The book examines nonlinear and linear systems in the state space form and through the transfer function method. It includes chapters on stability, controllability, observability, canonical forms, and system realizations. It also examines system design, Kalman filters, non-negative systems, adaptive control, and neural networks. This volume provides case studies drawn from electrical and mechanical engineering applications and includes problem sets and illustrative examples to enhance readers' assimilation of the material.

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