Presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms. This book discusses nonlinear and linear systems in the state space from and through the transfer function method; and stability, including marginal stability, asymptotical stability and global asymptotical stability.

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