Introduction to Mathematical Systems Theory

This is a book about modelling, analysis and control of linear time invariant systems. It uses the behavioural approach for which the authors are well regarded. It is a suitable text for senior undergraduates or beginning graduate students in mathematics and engineering and contains numerous exercises, including simulation problems and examples, notably of mechanical systems and electrical circuits.

Research into dynamical systems and control theory implications is a very hot topic J. Willems is well-known researcher and has a very good reputation in nonlinear control theory The book uses a unique behavioral approach for which the authors are well regarded Dynamical systems, controllability, observability and stability are among the many topics of active research that are presented Important, widely applicable modeling techniques are detailed Contains numerous exercises, simulation problems, and examples Will be of interest to applied mathematicians, mechanical and electrical engineers.

Inhalt
1 Dynamical Systems.- 2 Systems Defined by Linear Differential Equations.- 3 Time Domain Description of Linear Systems.- 4 State Space Models.- 5 Controllability and Observability.- 6 Elimination of Latent Variables and State Space Representations.- 7 Stability Theory.- 8 Time- and Frequency-Domain Characteristics of Linear Time-Invariant Systems.- 9 Pole Placement by State Feedback.- 10 Observers and Dynamic Compensators.- A Simulation Exercises.- A.1 Stabilization of a Cart.- A.2 Temperature Control of a Container.- A.3 Autonomous Dynamics of Coupled Masses.- A.4 Satellite Dynamics.- A.4.1 Motivation.- A.4.2 Mathematical modeling.- A.4.3 Equilibrium Analysis.- A.4.4 Linearization.- A.4.5 Analysis of the model.- A.4.6 Simulation.- A.5 Dynamics of a Motorbike.- A.6 Stabilization of a Double Pendulum.- A.6.1 Modeling.- A.6.2 Linearization.- A.6.3 Analysis.- A.6.4 Stabilization.- A.7 Notes and References.- B Background Material.- B.1 Polynomial Matrices.- B.2 Partial Fraction Expansion.- B.3 Fourier and Laplace Transforms.- B.3.1 Fourier transform.- B.3.2 Laplace transform.- B.4 Notes and References.- B.5 Exercises.- Notation.- References.