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Unknown input observer design for one-sided Lipschitz nonlinear systems. (English) Zbl 1345.93104

Summary: This paper considers the observer design problem for one-sided Lipschitz nonlinear systems with unknown inputs. The systems under consideration are a larger class of nonlinearities than the well-studied Lipschitz systems and have inherent advantages with respect to conservativeness. For such systems, we first propose a full-order nonlinear unknown input observer (UIO) by using the linear matrix inequality (LMI) approach. Following a similar design procedure and using state transformation, the reduced-order nonlinear UIO is also constructed. Sufficient conditions to guarantee existence of full-order and reduced-order UIOs are established by carefully considering the one-sided Lipschitz condition together with the quadratic inner-bounded condition. Based on the matrix generalized inverse technique, the UIO conditions are formulated in terms of LMIs. Moreover, the proposed observers are applied to a single-link flexible joint robotic system with unknown inputs. Simulation results are finally given to illustrate the effectiveness of the proposed design.

MSC:

93C41 Control/observation systems with incomplete information
93B07 Observability
93C10 Nonlinear systems in control theory
93C85 Automated systems (robots, etc.) in control theory
34H05 Control problems involving ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37M05 Simulation of dynamical systems
37N35 Dynamical systems in control
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