Superstabilization of Descriptor Continuous-Time Linear Systems via State-Feedback Using Drazin Inverse Matrix Method

Abstract

In this paper the descriptor continuous-time linear systems with the regular matrix pencil ( E , A ) are investigated using Drazin inverse matrix method. Necessary and sufficient conditions for the stability and superstability of this class of dynamical systems are established. The procedure for computation of the state-feedback gain matrix such that the closed-loop system is superstable is given. The effectiveness of the presented approach is demonstrated on numerical examples.

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

“…The main advantage of the presented approach is that it can be applied to the analysis of descriptor systems properties which are determined by matrix entries, such as positivity and superstability. This study is an extension of the results presented in [31].…”

“…We shall show that Equation ( 4) is equivalent to two equations (subsystems). Based on [3,31] we obtain the following. To simplify the notation we introduce…”

“…From the solution of Equation ( 23) it follows that Ā1α may contain insignificant entries that are further reduced through multiplication by x 0 ∈ Im Ē ĒD . To eliminate such entries from the matrix Ā1α we can use the term Ḡ(I n − Ē ĒD ), which does not change the solution to the state equation [3,31].…”

“…is given by (49) for FC defined by (72). It is easy to show [31] that the norm of (76) can be expressed by…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…An overview of state of the art in descriptor systems theory is given in [17][18][19][20]. Stability of this class of dynamical systems was investigated in [18,19,[21][22][23].…”