Non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay

The problem of non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay is discussed. Firstly, the form of non-fragile dynamic output feedback H∞ controller is given. Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously, Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique; Secondly, we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality, and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞ performance index γ, we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities, a sufficient condition for the existence of a non-fragile dynamic output feedback H∞ controller and satisfying the H∞ performance index γ is concluded for a class of uncertain switching systems with variable time delay; Finally, a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox.

Design and experimental realization of a backstepping nonlinear H∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach

This paper focuses on the development of a nonlinear [Formula: see text] control (NHC) algorithm for an autonomous underwater vehicle (AUV) in the vertical plane. A three-degree-of-freedom AUV depth model is developed in terms of a nonlinear affine form which is used to design the control algorithm. The depth is controlled using a backstepping technique which generates a desired pitch angle for the NHC algorithm. The nonlinear control is designed using the [Formula: see text]-gain analysis which is transformed into a Hamilton–Jacobi–Isaacs (HJI) inequality. Further, the HJI inequality is presented in terms of a nonlinear matrix inequality structure in order to find a solution for the NHC problem using the concept of convex optimization. Hence, we desire to test the convex property of the nonlinear system before the realization of the control algorithm. The robust behaviour of the NHC algorithm is realized by ensuring the performance of the proposed control algorithm in the face of model and parameter uncertainties. A comparison between the NHC algorithm and the state-dependent Riccati equation is made in order to show the efficacy of the developed control algorithm. Furthermore, an experimental study of the proposed control scheme has been pursued to analyse the effectiveness of the developed control algorithm.

Low Conservative Criteria for Robust Consensus of Multiagent Systems with Delays, Disturbances, and Topologies Uncertainties

Considering the limited communications conditions such as delays, disturbances, and topologies uncertainties, the stability criteria for robust consensus of multiagent systems are proposed in this paper. Firstly, by using the idea of state decomposition and space transformation, the condition for guaranteeing consensus is converted into verifying the robust stability of the disagreement system. In order to deal with multiple time-varying delays and switching topologies, jointly quadratic common Lyapunov-Krasovskii (JQCLK) functional is built to analyze the robust stability. Then, the numerical criterion can be obtained through solving the corresponding feasible nonlinear matrix inequality (NLMI); at last, nonlinear minimization is used like solving cone complementarity problem. Therefore, the linear matrix inequality (LMI) criterion is obtained, which can be solved by mathematical toolbox conveniently. In order to relax the conservativeness, free-weighting matrices (FWM) method is employed. Further, the conclusion is extended to the case of strongly connected topologies. Numerical examples and simulation results are given to demonstrate the effectiveness and the benefit on reducing conservativeness of the proposed criteria.

A DUAL-MODEL JUMPING FUZZY SYSTEM APPROACH TO NETWORKED CONTROL SYSTEMS DESIGN

A discrete-time jump fuzzy system with two hidden Markov models (HMMs) is proposed to portray the asymmetric network characteristic of a class of nonlinear networked control systems (NCSs) with random but bounded communication delays and packets dropout. The less conservative state feedback controller and the dual-model-depend guaranteed cost controller are designed base on the model. A homotopy- based iterative algorithm solving for nonlinear matrix inequality (NMI) is developed to get the control gains. Simulation examples are carried out to show the effectiveness of the proposed approaches.

DELAY-DEPENDENT ROBUST H∞ CONTROL FOR SINGULAR SYSTEMS WITH MULTIPLE DELAYS

This paper studies the problem of delay-dependent robust H∞ control for singular systems with multiple delays. Based on a Lyapunov–Krasovskii functional approach, an improved delay-dependent bounded real lemma (BRL) for singular time-delay systems is established without using any of the model transformations and bounding techniques on the cross product terms. Then, by applying the obtained BRL, a delay-dependent condition for the existence of a robust state feedback controller, which guarantees that the closed-loop system is regular, impulse free, robustly stable and satisfies a prescribed H∞ performance index, is proposed in terms of a nonlinear matrix inequality. The explicit expression for the H∞ controller is designed by using linear matrix inequalities and the cone complementarity iterative linearization algorithm. Numerical examples are also given to illustrate the effectiveness of the proposed method.