TY - JOUR
T1 - Stability and performance analysis of hybrid integrator–gain systems
T2 - A linear matrix inequality approach
AU - van den Eijnden, Sebastiaan
AU - Heemels, W.P.M.H.
AU - Nijmeijer, Henk
AU - Heertjes, Marcel
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2022/8
Y1 - 2022/8
N2 - Hybrid integrator–gain systems (HIGS) are nonlinear elements designed for overcoming fundamental limitations of linear time-invariant integrators. This paper presents numerically robust conditions for time-domain stability and performance of HIGS-controlled systems. In particular, using piecewise quadratic (PWQ) Lyapunov functions defined over polyhedral subregions of the state-space, conditions for stability and computations of upper-bounds on the L2-gain and H2-norm are formulated as convex optimization problems in terms of numerically tractable linear matrix inequalities (LMIs). In order to improve accuracy and robustness, the LMIs are constructed in a manner to eliminate explicit equality constraints typically related to continuity of the PWQ functions. Novel conditions are presented that guide further refinement of the subregions over which the PWQ Lyapunov functions are defined in order to increase the accuracy of the approach. The effectiveness of the presented analysis tools is demonstrated through a numerical case-study on a motion system.
AB - Hybrid integrator–gain systems (HIGS) are nonlinear elements designed for overcoming fundamental limitations of linear time-invariant integrators. This paper presents numerically robust conditions for time-domain stability and performance of HIGS-controlled systems. In particular, using piecewise quadratic (PWQ) Lyapunov functions defined over polyhedral subregions of the state-space, conditions for stability and computations of upper-bounds on the L2-gain and H2-norm are formulated as convex optimization problems in terms of numerically tractable linear matrix inequalities (LMIs). In order to improve accuracy and robustness, the LMIs are constructed in a manner to eliminate explicit equality constraints typically related to continuity of the PWQ functions. Novel conditions are presented that guide further refinement of the subregions over which the PWQ Lyapunov functions are defined in order to increase the accuracy of the approach. The effectiveness of the presented analysis tools is demonstrated through a numerical case-study on a motion system.
KW - H-norm
KW - Hybrid integrator–gain system
KW - L-gain
KW - Linear matrix inequality (LMI)
UR - http://www.scopus.com/inward/record.url?scp=85126577264&partnerID=8YFLogxK
U2 - 10.1016/j.nahs.2022.101192
DO - 10.1016/j.nahs.2022.101192
M3 - Article
AN - SCOPUS:85126577264
SN - 1751-570X
VL - 45
JO - Nonlinear Analysis: Hybrid Systems
JF - Nonlinear Analysis: Hybrid Systems
M1 - 101192
ER -