Popov-H∞ Robust Path-Tracking Control of Autonomous Ground Vehicles with Consideration of Sector Bounded Kinematic Nonlinearity

This paper proposes a new approach to cope with the kinematic nonlinearity in the H∞ vehicle path-tracking controller synthesis problem. The kinematic nonlinearity presented in the vehicle lateral error state is found to satisfy the sector-bound condition. By isolating the sector bounded nonlinearity via an upper linear fractional transformation (LFT), a Lur'e system is formulated. A nominal robust controller is synthesized to meet both the Popov-H∞ criterion and the regional pole placement requirement. A polytopic gain-scheduling technique is subsequently employed to accommodate the effect of the varying vehicle longitudinal velocity. Finally, an instant-turning maneuver and a sharp lane-changing maneuver are tested in CarSim-Simulink joint simulations whose results demonstrate the superiority of the proposed Popov-H∞ controller over a conventional H∞ controller.

New stability conditions for class of nonlinear discrete-time systems with time-varying delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

New stability conditions for class of nonlinear discrete-time systems with time-varying delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

New stability conditions for a class of nonlinear discrete-time systems with time-varying delay

The problem of stability analysis for a class of nonlinear discrete time systems with time varying delay is studied in this work. Such systems are modeled by delayed difference equations. Subsequently, this system is transformed into an arrow form matrix representation. Using M-matrix properties, novel sufficient stability conditions are determined. It is shown how to use our method to design a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of a nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Several examples are provided to show the effectiveness of the introduced technique. <br>

On Delay-dependent and Delay-derivative-dependent Stability and Stabilization for Lur’e Systems with Slow-varying Delay

This note is concerned with the absolute stability for time-varying delay Lur’e system with sector-bounded nonlinearity. Improved delay-dependent and delay-derivative-dependent stability criteria are obtained in the form of linear matrix inequalities (LMIs) by constructing a modified augmented Lyapunov-Krasovskii (LK) functional without applying the model transformation or the bounding techniques for cross terms. Thus, the presented delay-dependent criteria are less conservative than those in the literature. Moreover, state feedback stabilizing controllers based on the proposed stability criteria are designed. Numerical example demonstrates the effectiveness and superiority of the proposed method.

Stabilization of systems with sector bounded nonlinearity by a sawtooth sampled-data feedback

The paper considers a nonlinear Lur’e type system with a sector bounded nonlinearity. The zero equilibrium of the system may be unstable, so it is stabilized by a periodically sampled feedback signal. Such stabilization problems were previously explored by a number of researches with the help of the zero-order hold (ZOH) control that is kept constant between successive sampling times. The main disadvantage of this method is that the time delay introduced by ZOH has a destabilizing impact on the closed feedback system, especially in the case when the sampling frequency is sufficiently low and the feedback gain is high. To reduce this effect it is proposed to modify the form of the stabilizing signal. In this paper the reverse sawtooth control is introduced instead of ZOH. The stability criterion is obtained in the form of a feasibility problem for some linear matrix inequalities (LMI). A numerical example demonstrates how the new stabilization method allows to reduce the sampling frequency required for stabilization.