Controllability of dynamical systems

Abstract

The paper contains systems descriptions and fundamental results concerning the solution of the most popular linear continuous-time control models with constant coefficients. First, different kinds of stability are discussed. Next fundamental definitions of controllability both for finite-dimensional and infinite-dimensional systems are recalled and necessary and sufficient conditions for different kinds of controllability are formulated. Moreover, fundamental definitions of controllability both for finite-dimensional and infinite-dimensional control systems are presented and necessary and sufficient conditions for different kinds of controllability are given. Finally, concluding remarks and comments concerning possible extensions are presented.

Controllability of second‐order Sobolev‐type impulsive delay differential systems

“…In the recent years, study of controllability for dynamical systems has generated a great interest among researchers because of demonstrating applications. The theory of controllability for finite dimensional linear systems is extensively discussed by Klamka . Moreover, differential systems with delay are used frequently in many fields such as 3‐D printing and oil drilling, modeling of systems, panorama of natural phenomena, and porous media.…”

“…The theory of controllability for finite dimensional linear systems is extensively discussed by Klamka. 10 Moreover, differential systems with delay are used frequently in many fields such as 3-D printing and oil drilling, modeling of systems, panorama of natural phenomena, and porous media. The authors Arthi and Balachandran 4 and Jeet and Bahuguna, 11 offered adequate analysis to deal with the evolutions systems with delay.…”

Minimum Energy Control of Descriptor Fractional Discrete–Time Linear Systems with Two Different Fractional Orders

“…This subject has been considered in many papers and monographs (Kaczorek and Klamka, 1986;Kaczorek, 2014;Klamka, 1991;2009;2014). LTI (linear time-invariant) systems theory deals with numerous types of systems, e.g., positive (Kaczorek 2002;2013a;2013c;2011d), descriptor (Campbell et al, 1976;Dai 1989;Dodig and Stosic, 2009;Guang-Ren, 2010;Van Dooren, 1979;Van Dooren and Beelen, 1988) or fractional (Nishimoto, 1984;Oldham and Spanier, 1974;Podlubny, 1999).…”

Relationship between the observability of standard and fractional linear systems

“…Those notions are the basic concepts of the modern control theory [1,6,13,16,21,24,25]. They have been extended to positive and fractional linear and nonlinear systems [2, 4, 5, 7-11, 22, 23].…”