On Analytical Approximation of the Maximal Invariant Ellipsoids for Linear Systems With Bounded Controls

• Published in: IEEE transactions on automatic control Vol. 54; no. 2; pp. 346 - 353
• Main Authors: Zhou, Bin, Duan, Guang-Ren
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Applied sciences; Approximation; Asymptotic stability; Automatic control; Computer science; control theory; systems; Control equipment; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Convergence; Delay; Ellipsoids; Exact sciences and technology; Feedback; Frequency domain analysis; Invariants; Linear systems; Mathematical analysis; Modelling and identification; nonlinear systems; Read only memory; Ricatti equations; Stability; Teleoperators; Invariant; Necessary and sufficient condition; Saturation; Non linear control; Control synthesis; Ricatti equations; Non linear system; Linear control; Asymptotic stability; nonlinear systems; Linear time invariant system; Riccati equation; Ellipsoid; Actuator
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.2007879

Analytical approximation of the maximal invariant ellipsoids for linear systems with actuator saturation is established. Simultaneously, a necessary and sufficient condition for such approximation equalling to the exact maximal invariant ellipsoid is presented. In addition, a geometric property of the maximal invariant ellipsoid in ldquominimal energy control with guaranteed convergence raterdquo problem is proposed. All results are given in explicit forms and easy to implement in system analysis and design. Two numerical examples are used to show the effectiveness of the proposed approach.