Asymptotic stability analysis of nonlinear real-time networked control systems

The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.     

Gait planning for quadruped robot based on dynamic stability: landing accordance ratio

In this article, the method for increasing dynamic stability of quadruped robot is proposed. Previous researches on dynamic walking of quadruped robots have used only walking pattern called central pattern generator (CPG). In this research, different from walking generation with only CPG, a instinctive stability measure called landing accordance ratio, is proposed and used for increasing dynamic stability. In addition, dynamic balance control and control to adjust walking trajectory for increasing dynamic stability measure is also proposed. Proposed methods are verified with dynamic simulation and a large number of experiments with quadruped robot platform.     

Intuitive robust stability metric for PID control of self-regulating processes

Published methods establish how plant-model mismatch in the process gain and dead time impacts closed-loop stability. However, these methods assume no plant-model mismatch in the process time constant. The work presented here proposes the robust stability factor metric, RSF, to examine the effect of plant-model mismatch in the process gain, dead time, and time constant. The RSF is presented in two forms: an equation form and a visual form displayed on robustness plots derived from the Bode and Nyquist stability criteria. This understanding of robust stability is reinforced through visual examples of how closed-loop performance changes with various levels of plant-model mismatch. One example shows how plant-model mismatch in the time constant can impact closed-loop stability as much as plant-model mismatch in the gain and/or dead time. Theoretical discussion shows that the impact is greater for small dead time to time constant ratios. As the closed-loop time constant used in Internal Model Control (IMC) tuning decreases, the impact becomes significant for a larger range of dead time to time constant ratios. To complete the presentation, the RSF is used to compare the robust stability of IMC-PI tuning to other PI, PID, and PID with Filter tuning correlations.     

Robustness with dynamic IQCs: An exact state-space characterization of nominal stability with applications to robust estimation

For robustness analysis with integral quadratic constraints, we formulate a new positivity condition on the solution of the corresponding linear matrix inequality which is necessary and sufficient for nominal stability of the underlying system. The application of this technical result is illustrated by a complete solution of the L₂-gain and robust H₂-estimator design problems if the uncertainties are characterized by dynamic integral quadratic constraints.     

Necessary and sufficient stability condition of fractional-order interval linear systems

This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1≤α<2. Using the existence condition of Hermitian P=P^∗ for a complex Lyapunov inequality, we prove that the fractional-order interval linear system is robust stable if and only if there exists Hermitian matrix P=P^∗ such that a certain type of complex Lyapunov inequality is satisfied for all vertex matrices. The results are directly extended to the robust stability condition of fractional-order interval polynomial systems.     

Fuzzy motion control strategy for cooperation of multiple automated vehicles with passengers comfort

This paper considers motion control for a cooperative system of automated passenger vehicles. It develops a cooperative scheme based on a decentralized planning algorithm which considers the vehicles in an initial open chain configuration. In this scheme the trajectories are intersections-free, and each trajectory is planned independently of the others. To ensure the stabilization of each vehicle in the planned trajectory, a fuzzy closed loop motion control is presented, where, based on the properties of the Fuzzy maps, the Lyapunov’s stability of the motion errors is demonstrated for all the vehicles. Based on the ISO 2631-1 standard, the saturation property of the Fuzzy maps guarantees low values of longitudinal and lateral accelerations, to ensure comfort of the human body during the motion. The validity of this control algorithm is supported by simulation experiments.     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

Nonlinear gliding stability and control for vehicles with hydrodynamic forcing

This paper presents Lyapunov functions for proving the stability of steady gliding motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov function is constructed using a conservation law discovered by Lanchester in his classical work on phugoid-mode dynamics of an airplane. The phugoid-mode dynamics, which are cast here as Hamiltonian dynamics, correspond to the slow dynamics in a multi-time-scale model of a hydro/aerodynamically-forced vehicle in the longitudinal plane. Singular perturbation theory is used in the proof of stability of gliding motions. As an intermediate step, the simplifying assumptions of Lanchester are made rigorous. It is further shown how to design stabilizing control laws for gliding motions using the derived function as a control Lyapunov function and how to compute the corresponding regions of attraction.     

Stability analysis of a class of digital filters utilizing single saturation nonlinearity

A novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented. An example showing the effectiveness of the present criterion is given.