Robust stabilization of linear systems in the presence of Gaussian perturbation of parameters

✍ Scribed by Saroj K. Biswas

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 196 KB
• Volume: 19
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/(sici)1099-1514(199807/08)19:4<271::aid-oca631>3.0.co;2-u

✦ Synopsis

Stabilization of linear systems in state space in the presence of parametric perturbations is considered. The perturbed system is represented by a matrix differential equation with the elements of the matrices given by Gaussian processes with known mean and covariance. Using methods from stochastic control theory, certain pole-placement-like results are derived which hold in the mean square sense. In the absence of any perturbation, these results reduce to the well-known results of pole placement for deterministic linear systems. Minimizing the real part of the largest eigenvalue of the expected closed-loop matrix, we obtain the optimal feedback gain that stabilizes the system at the fastest possible rate. The question of existence of a guaranteed stabilizing feedback is also investigated. As a consequence of the main result we obtain a method of designing fault-tolerant systems that will survive in the events of catastrophic controller failure. An extension of the Luenberger observer for uncertain systems is also presented.