TY - JOUR
T1 - Dissipative state observer design for nonlinear time-delay systems
AU - Avilés, Jesús D.
AU - Moreno, Jaime A.
AU - Bejarano, Francisco J.
N1 - Publisher Copyright:
© 2022 The Franklin Institute
PY - 2023/1
Y1 - 2023/1
N2 - This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI's) or linear matrix inequalities (LMI's). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.
AB - This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI's) or linear matrix inequalities (LMI's). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.
UR - http://www.scopus.com/inward/record.url?scp=85145647232&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2022.11.048
DO - 10.1016/j.jfranklin.2022.11.048
M3 - Artículo
AN - SCOPUS:85145647232
SN - 0016-0032
VL - 360
SP - 887
EP - 909
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 2
ER -