Mathematica implementation of output-feedback pole assignment for uncertain systems via symbolic algebra

Quadrotor Angle Stabilization using Full State Feedback by Partial Robust Pole Assignment Method: Pole Retention

“…Robust partial pole assignment consists of a few steps and iteration to determine all the stabilizing feedback gain coefficients in a similar way to "Pole Retention" [10]. This way, both the stability and a good response is maintained while designing the state feedback.…”

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

“…Some related research studies which have been accomplished in this field can be considered as follows: improvement of the dynamic performance of power systems (Sattar 2006), stabilisation of individual generators with statefeedback-controlled SVCs through pole assignment (Zhou 2010), disturbance attenuation in multivariable linear systems (Duan, Irwin, and Liu 2000), design of reconfigurable control system (Esna Ashari, Khaki Sedigh, and Yazdanpanah 2005), extension of the state-feedback design for linear distributed parameter systems and robust stability of linear large-scale systems using eigenstructure assignment (Labibi, Lohmann, Khaki Sedigh, and Jabedar Maralani 2001;Deutscher and Harkort 2009), pole structure assignment in implicit, linear and uncontrollable systems (Loiseau and Zagalak 2009), application of symbolic algebra techniques for implementing output-feedback pole assignment algorithms for uncertain systems (Zheng, Zolotas, and Wang 2006), robust pole placement (Kautsky, Nichols, and Van Dooren 1985;Benzaouia, Mesquine, Naib, and Hmamed 2001), optimal pole assignment for discrete-time linear systems (Zhou, Li, Duan, and Wang 2009), static output feedback pole assignment (Carotenuto, Franze`, and Muraca 2001;Franze`, Carotenuto, and Muraca 2005;Bachelier, Bosche, and Mehdi 2006;Yang and Orsi 2007), numerical algorithm for an eigenvalue assignment problem which arises from a singular system (Chu and Ho 2002), pole placement of continuous linear time-invariant (LTI) systems by means of suboptimal periodic feedback in which a performance index is minimised (Lavaei, Sojoudi, and Aghdam 2010), robust pole assignment in high-order descriptor linear systems (Duan and Yu 2008), and examination of the sensitivity of the pole assignment (Higham, Konstantinov, Mehrmann, and Petkov 2004). As it is seen, in parallel with application research studies, many studies have been performed for improving the theoretical bases of these methods and also overcoming the probable drawbacks which may be encountered in some practical cases.…”

Special issue on the use of computer algebra systems for computer aided control system design

“…So¨ylemez and Ustoglu (2006) present some classical control examples that illustrate the advantages of the computer algebra in the process of control system design, focusing to block diagram reduction, calculation of stabilizing compensators, dominant pole assignment and robust pole assignment. Zheng et al (2006) present the application of symbolic algebra techniques to the Mathematica implementation of a set of output-feedback pole assignment algorithms, for systems characterized by parametric uncertainty. Karcanias et al (2006) emphasize the significance of hybrid computations (mixed numerical and symbolic computations) in complex problems such as the computation of the greatest common divisor (GCD) of several polynomials that emerges in many fields of applications.…”