Robust Control of Jump Linear Stochastic Systems Applications to Sampled-Data Control

This monograph concentrates on the theory of robust control of linear impulsive stochastic systems and stochastic systems with jumps. It discusses theoretical points concerned with impulsive stochastic systems including optimal control, robust stabilization, and H2- and Hinfinity-type results. Considering the major role played by the impulsive Lyapunov and impulsive Riccati equations in these problems, the book presents a thorough treatment of these equations in a general framework. It also presents various applications to sampled-data control.

Robust Control of Jump Linear Stochastic Systems is a self-contained and clearly structured presentation of up-to-date research in this area, relevant to researchers in control theory and to non-specialists who are interested in the theory of robust control of linear impulsive stochastic systems. Theoretical and applied mathematicians, research engineers, and graduate students in the aforementioned fields will also find value in this book.

1. Preliminaries.- 2. Linear Differential Equations with Jumps Generating a Positive Evolution on an Ordered Banach Space.- 3. Stability of Systems of Stochastic Linear Differential Equations with Jumps.- 4. Structural Properties of Linear Stochastic Systems with Jumps.- 5. A Class of Generalized Matrix Riccati Differential Equations with Jumps.- 6. Linear Quadratic Optimal Control Problems for Linear Stochastic Systems with Jumps.- 7. H2 Optimal Control and H2 Optimal Filtering for Stochastic Linear Systems with Jumps.- 8. Robust Control with Respect to the Parametric Uncertainties of a Stochastic Linear System with Jumps.

Vasile Dragan received his undergraduate degree in mathematics in 1974 and his Ph.D. in 1979, from University of Bucharest, Faculty of Mathematics. He is now senior researcher at the Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, Department of Differential Equations and Optimal Control. His research interests are in qualitative theory of differential equations mainly in singular perturbation techniques, stability theory and asymptotic expansions. He is also currently interested in control theory, robust control for deterministic and stochastic systems for finite dimensional and infinite dimensional systems both in time invariant and time-varying cases, H2 and H8 filtering, numerical methods for Riccati equations in deterministic and stochastic linear quadratic differential games. He is the author or coauthor of six books and over 200 scientific papers, dedicated to various topics on Differential Equations and Control Theory. In 1994, the Romanian Academy awarded him ‘Gheorghe Lazar’ prize for the papers published in control field. He is a member of the American Mathematical Society. Since 2017, he has been a member of the Academy of the Romanian Scientists. He is Associate Editor of the IET Control Theory and Applications journal, International Journal of Innovational Computing, Information and Control and of the ICIC-Express Letters.

Samir Aberkane received his M.Sc. degree in control engineering from the Institut National Polytechnique de Lorraine and his Ph.D. degree in Automatic Control from Henri Poincaré University, in 2003 and 2006 respectively. In 2007, he held a Post-Doctoral position at Université Libre de Bruxelles, Belgium. He is currently an associate professor at Lorraine University. His current research interests include robust control and filtering of stochastic systems and stochastic game theoretical Riccati equations.

 Ioan-Lucian Popa received double M.Sc. Degree in Mathematics and Computer Science, in 2004 and 2006, respectively, and his Ph.D. Degree in Mathematics from West University of Timisoara, Romania in 2012. He is currently a senior lecturer at the ‘‘1 Decembrie 1918’’ University of Alba Iulia, Romania. His current research interests include topics in dynamical systems, stability, optimal control and filtering. He was the recipient of the 2017 “Professor Bologna” Teaching Excellence Award granted by National Alliance of Student Organizations in Romania (ANOSR). He is the author of a research monograph, co-authored 5 didactic books and over 40 scientific papers.