Set-Invariance-based Interpretations for the L1 Performance of Nonlinear Systems with Non-unique Solutions
- Set-Invariance-based Interpretations for the L1 Performance of Nonlinear Systems with Non-unique Solutions
- Choi, Hyung Tae; KIM, JUNG HOON
- Date Issued
- John Wiley & Sons Inc.
- This paper is concerned with tackling the L1 performance analysis problem of continuous
and piecewise continuous nonlinear systems with non-unique solutions by
using the involved arguments of set-invariance principles. More precisely, this paper
derives a sufficient condition for the L1 performance of continuous nonlinear systems
in terms of the invariant set. With respect to the case such that solving a
nonlinear differential equation is difficult and thus an employment of the invariant
set-based sufficient condition is a non-trivial task, we also derive another sufficient
condition through the extended invariance domain approach. Because this extended
approach characterizes set-invariance properties in terms of the corresponding vector
field and an extended version of contingent cones, the L1 performance analysis
problem could be solved without considering both the explicit solutions for the differential
equation and the relevant solution uniqueness. These arguments associated
with the L1 performance of continuous systems are further extended to the involved
case of piecewise continuous nonlinear systems, and we establish parallel results
relevant to the set-invariance principles obtained for the continuous nonlinear systems.
Finally, numerical examples are provided to demonstrate the effectiveness as
well as the applicability of the overall results derived in this paper.
- Article Type
- International Journal of Robust and Nonlinear Control, 2022-12
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