Suboptimal l∞ → l∞ Control of Switched Linear Models: a Superstability Approach*. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Cheng, Y.; Ozbay, B.; Sznaier, M.; Lagoa, C.
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 14380
• Page End: 14385
• Publication Date: 2017-07
• Subjects: Control of Switched Systems -- Disturbance Rejection -- Convex Optimization; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.2433
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper we consider the problem of designing an observer-based controller for switched linear systems under arbitrary switching, with guaranteed l∞ → l∞ performance. It is shown that, by using the concepts of polyhedral Lyapunov functions and superstability, the problem can be recast into a nonconvex constrained Polynomial Optimization Problem (POP). In turn, this problem can be relaxed into a sequence of convex Semi-Definite Programs (SDPs) by resorting to moments-based polynomial optimization techniques. Further, by exploiting the sparsity pattern exhibited by the problem, we show that the original POP can be equivalently reformulated as an SDP problem with a rank-1 constraint. An efficient algorithm is proposed to solve the later, by seeking low rank solution through re-weighted nuclear norm minimization.