The importance of the algebraic Riccati equation (ARE) in control and communication engineering cannot be overstated. However, existence of ARE depends crucially on non-singularity of certain parameter matrices - known as the "regularity condition". It is known that solutions of the ARE are nothing but some kind of (generalized) stored energy within the system, called "storage functions". Existence of storage functions is a property known as dissipativity. Arguably, dissipativity is a system's inherent property, and hence, it ought to be independent of whether the system's parameter matrices are satisfying the regularity condition or not. The question is: if the ARE does not exist, how then do we get its solution - the storage function? In this talk we shall try to investigate this case of "singular" dissipative systems. We shall see how the resolution of this conundrum lies within a generalization of the so called Hamiltonian matrix to a corresponding Hamiltonian system. We shall also see some remarkable consequences of this resolution.
Debasattam Pal received his Bachelor of Engineering (B.E.) degree from the Department of Electrical Engineering of Jadavpur University, Kolkata, in 2005. He received his M.Tech. and Ph.D. degrees from the Department of Electrical Engineering, IIT Bombay, in the years 2007 and 2012, respectively. He then worked as an Assistant Professor in IIT Guwahati from July, 2012 to May, 2014. After that, he joined IIT Bombay in June, 2014, as an Assistant Professor in the EE Department. His main area of research is systems and control theory. More specifically, his areas of interest are: multidimensional systems theory, algebraic analysis of systems, dissipative systems, optimal control and computational commutative algebra.