Tracking Control of Linear Systems

The primary purpose of control is to force desired behavior in an unpredictable environment, under the actions of unknown, possibly unmeasurable disturbances and unpredictable, and therefore probably nonzero, initial conditions. This means that tracking and tracking control synthesis are fundamental control issues. Surprisingly, however, tracking theory has not been well developed, and stability theory has dominated. Tracking Control of Linear Systems presents the fundamentals of tracking theory for control systems. The book introduces the full transfer function matrix F(s), which substantially changes the theory of linear dynamical and control systems and enables a novel synthesis of tracking control that works more effectively in real environments.An Introduction to the New Fundamentals of the Theory of Linear Control SystemsThe book begins by re-examining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: input-output (IO) control systems and input-state-output (ISO) control systems. The book also discusses the fundamentals of tracking and trackability. It presents new Lyapunov tracking control algorithms and natural tracking control (NTC) algorithms, which ensure the quality of the tracking under arbitrary disturbances and initial conditions. This natural tracking control is robust, adaptable, and simple to implement.Advances in Linear Control Systems Theory: Tracking and TrackabilityThis book familiarizes readers with novel, sophisticated approaches and methods for tracking control design in real conditions. Contributing to the advancement of linear control systems theory, this work opens new directions for research in time-invariant continuous-time linear control systems. It builds on previous works in the field, extending treatment o

On Control Systems Classic Fundamentals: Introduction. Control Systems. System Regimes. Transfer Function Matrix G(s). Novel System Fundamental: Full Transfer Function Matrix F(S): Problem Statement. Nondegenerate Matrices. Full Transfer Function Matrix F(s). Novel Control Theories: Tracking and Trackability: Tracking Theory. Trackability Theory. Novel Synthesis of Tracking Control: Linear Tracking Control (LITC). Lyapunov Tracking Control (LTC). Natural Tracking Control (NTC). NTC versus LTC. Conclusion: On F(s). On Tracking and Trackability. On Tracking Control. Recommendation. Appendixes: Notation. From IO system to ISO system. From ISO system to IO system. Proof of Theorem 64. Proof of Theorem 67. Proof of Theorem 72. Proof of Theorem 91. Proof of Lemma 102-Basic Lemma. Proof of Theorem 116. Proof of Theorem 142. Proof of Theorem 145. Proof of Theorem 149. Author Index. Subject Index.

Gruyitch, Lyubomir T.