TY - JOUR

T1 - Quadratic Performance Analysis of Switched Affine Time-Varying Systems

AU - Li, Wenzhi

AU - Huang, Chi

AU - Zhai, Guisheng

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

AB - We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

KW - differential LMIs

KW - L2 gain

KW - observers

KW - quadratic stabilization

KW - switched affine systems

KW - switching law

KW - time-varying systems

KW - tracking

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U2 - 10.2478/amcs-2018-0032

DO - 10.2478/amcs-2018-0032

M3 - Article

AN - SCOPUS:85054853317

VL - 28

SP - 429

EP - 440

JO - International Journal of Applied Mathematics and Computer Science

JF - International Journal of Applied Mathematics and Computer Science

SN - 1641-876X

IS - 3

ER -