A new approach to solve the continuous-time linear descriptor systems based on generalized upper triangular form and positivity criteria

The present study addresses two main problems of descriptor systems. First, the state response of the continuous-time linear descriptor systems using a new, different method from the previous ones is obtained. For this purpose, this paper take advantage of the generalized Sylvester equation and generalized upper triangular form. Second, the positivity of responses is studied. To inspect the positivity, necessary and sufficient conditions are elicited. The conditions are investigated by some numerical examples, and their diagrams are plotted with Simulink in MATLAB.