Linear Continuous-Time Systems

The book aims to unify the study and applications of the IO, ISO, and IIO linear continuous-time time-invariant systems and highlight its importance for analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text investigates a complex domain fundamental dynamical characteristic of the systems. It presents the definition of F(s) and resolves the problem of its determination so that it has the same properties as the well-known system transfer function matrix G(s). Additionally, the reader will explore the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions.

This book aims to help the reader understand the linear continuous-time time-invariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuous-time time-invariant systems, for short systems.