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 method

Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stability

Controllability

Observability

Canonical forms

System realizations and minimal realizations, including state space approach and transfer function realizations

System design

Kalman filters

Nonnegative systems

Adaptive control

Neural networks
The 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 studies

Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter

Illustrative examples in all the chapters

An introduction and analysis of new stability concepts

An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first edition
Although 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.