Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...

Linear constant-coefficients control systems with output on arbitrary time scales are studied. Kalman criteria of controllability and observability are extended to such systems. The main problem is to find criteria for an abstract input/output map to have a realization as a system on the time scale. Two different characterizations of realizability are proved. They extend the classical results o...

There exist many good books on linear systems. I wish to mention here only some of them: L. Among these volumes the book by P.J. Antsaklis and A.M. Michel occupies a special place. It is an interesting and original introduction to modern control systems theory. It contains also many interesting problems from advanced systems theory. According to the authors the primary aim of the book is the fo...

1. Linear Multivariable Systems 1.1. Emergence of State Space Approach 1.2. Discrete-time Control 1.3. Riccati Equation and Stabilization for Continuous-time Systems 1.4. Design Procedure 1.5. Static Output Feedback and Dynamic Compensation 1.6. Servo Control and Internal Model Principle 1.7. Design and Analysis based on Frequency Response 1.8. Control System Example 2. Control System Example 2...

In this paper, we provide an overview of some control synthesis methodologies for boundary systems (BCS) in port-Hamiltonian form. At first, it is shown how to design a state-feedback action able shape the energy function move its minimum at desired equilibrium, and achieve asymptotic stability via damping injection. Secondly, general conditions that linear regulator has satisfy have well-posed...

We show how homological algebra and algebraic analysis allow to give various notions of equivalence for linear control systems which do not depend on their presentations and therefore preserve their structural properties.