Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

In this paper, the problem of asynchronous robust H_∞ dynamic output feedback control for Markovian jump neural networks with norm-bounded parameter uncertainties and mode-dependent time-varying delays is investigated. The improved delay-dependent stochastic stability conditions and bounded real lemma are obtained by introducing the relaxation variables, which reduces the conservatism caused by boundary technology and model transformation. An improved Lyapunov-Krasovskii functional is constructed using linear matrix inequalities. On this basis, the solution of robust H_∞ dynamic output feedback problem and sufficient conditions for solving the problem of asynchronous dynamic output feedback controller are given respectively. Asynchronous dynamic output feedback controller is constructed to ensure that the closed-loop mode-dependent time-varying delays Markovian jump neural networks achieve different convergence speeds. The given H_∞ performance index is satisfied for the delays not bigger than a given upper bound. Numerical examples are employed to show the effectiveness and correctness of the method presented in this paper.

     

Robust static output feedback control for linear discrete-time systems with time-varying uncertainties

This paper is concerned with the problem of designing robust static output feedback controllers for linear discrete-time systems with time-varying polytopic uncertainties. Sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities, and the results are extended to H₂ and H_∞ static output feedback controller designs. Numerical examples are given to illustrate the effectiveness of the proposed design methods.     

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

H ∞ output feedback stabilisation of linear discrete-time systems with impulses

This article addresses the issue of designing an H _∞ output feedback controller for linear discrete-time systems with impulses. First, a new concept of H _∞ output feedback stabilisation for general linear discrete-time systems with impulses is introduced. Then sufficient linear matrix inequality conditions for the stabilisation and H _∞ performance of general discrete systems with impulses are proposed. In addition, the result is applied to resolve typical output feedback control problems for systems with impulses, such as the decentralised H _∞ output feedback control and the simultaneous H _∞ output feedback control. Finally, a numerical simulation is also presented to illustrate the effectiveness of the proposed results.     

Extended time-frequency conditions for the Instability of a class of non-linear time-varying systems

This paper presents new criteria for the L ₂-input, L ₂-output stability of a class of feedback systems containing a time-invariant convolution operator and a time varying non-linearity in cascade, in a negative feedback loop. These are sufficient conditions for the system stability derived using the multiplier concept and involve certain time-domain conditions on the multiplier. The method of derivation draws on the theory of positivity of compositions of operators and time-varying gains and necessitates an upper bound on the rate of variation of the time-varying gain.     

Output‐Feedback Control for Continuous‐time Interval Positive Systems under L1 Performance

This paper is concerned with the design of an L₁‐induced output‐feedback controller for continuous‐time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L₁‐induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output‐feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single‐input‐multiple‐output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L₁‐induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.     

H∞-control for semilinear systems in Hilbert spaces

This paper considers the H_∞-controlled with state feedback for semilinear infinite-dimensional systems in a Hilbert space. Necessary and sufficient conditions for the existence of a suboptimal H_∞ controller are derived in terms of a Hamilton-Jacobi equation.     

Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays

This paper focuses on the problems of globally exponential stability and stabilization with H_∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H_∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.     

Improved LMI conditions for H ∞ output feedback stabilization of linear discrete-time systems

The problem of H _∞ output feedback control for discrete-time systems is investigated in this paper. The main contribution is to provide a uniform framework for generating sufficient linear matrix inequality conditions. Those conditions are classified into two parallel parts based on the way of slack variable selection. Moreover, it is shown that the existing result is a special case of the new conditions by taking few of the additional free matrix parameters to be zero. This directly leads to more flexibility and less conservativeness in the H _∞ output feedback control design. Numerical examples are carried out for illustration.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H _∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H _∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler’s lemma and Dualization lemma, some novel conditions for exponential H _∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.     

Stabilisation and H∞ control of neutral stochastic delay Markovian jump systems

This paper investigates the exponential stabilisation and H_∞ control problem of neutral stochastic delay Markovian jump systems. First, a delay feedback controller is designed to stabilise the neutral stochastic delay Markovian jump system in the drift part. Second, sufficient conditions for the existence of feedback controller are proposed to ensure that the resulting closed-loop system is exponentially stable in mean square and satisfies a prescribed H_∞ performance level. Finally, numerical examples are provided to show the effectiveness of the proposed design methods.     

Cooperative containment of discrete‐time linear multi‐agent systems

This paper investigates the cooperative containment control problem for discrete‐time multi‐agent systems with general linear dynamics. Distributed containment control protocols on the basis of state feedback design and output feedback design are proposed. Necessary and sufficient conditions are presented for both the state feedback and output feedback cases, which are less conservative than those in the literature. These conditions depend on the spectral properties of the topology matrix. Then, effective algorithms are proposed to obtain control gain matrices for both cases based on H _∞ type Riccati design. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Pole-assignment with periodic output feedback: computer assisted study on a 2-dimensional linear system

In this paper we study the single-input single-output discrete time linear system where X_k ∈ R², and where the input u_k is defined by the time-varying output feedback We examine conditions under which the system using periodic output feedback can have its closed-loop poles arbitrarily assigned.     

Event‐triggered output feedback H∞ control for networked control systems

This paper investigates event‐triggered output feedback H_∞ control for a networked control system. Transmitted through a network under an event‐triggered scheme, the sample outputs of the plant are used to drive the dynamical output feedback controller to generate a new control signal in the discrete‐time domain. The discrete‐time control signals are also transmitted through the network to drive the plant. As a result of two types of transmission delays, the controlled plant and the dynamical output feedback controller are driven by the discrete‐time outputs and control signals at different instants of time. An interval decomposition method is introduced to place the controlled plant and the output feedback controller into the same updated time interval but with updated signals at different instants. Based on a proper Lyapunov‐Krasovskii functional, sufficient conditions are derived to ensure H_∞ performance for the controlled plant. Finally, numerical simulations are used to demonstrate the practical utility of the proposed method.     

Observer-based Non-fragile Mixed Passivity and H∞ Feedback Control for Fuzzy Stochastic Jump System Subject to Quantized Measurements

This paper considers the topic of the observer-based non-fragile mixed passivity and H_∞ state feedback control for time-varying delay and norm-bounded parameter uncertainties fuzzy stochastic Markovian jump system subject to quantized measurements. The aim of this paper is to provide a suitable observer-based non-fragile state feedback controller to enhance stochastic stabilization of the closed-loop system and satisfy mixed passivity and H_∞ performance. By constructing mode-dependent Lyapunov-Krasovskii functional, novel conditions are achieved in virtue of linear matrix inequalities. Two examples including truck-trailer model are given to illustrate the effectiveness of the developed method.

     

Distributed robust control of uncertain linear multi‐agent systems

In this paper, the distributed H _∞ robust control problem synthesized with transient performance is investigated for a group of autonomous agents governed by uncertain general linear node dynamics. Based on the relative information between neighboring agents and some information of other agents, distributed state‐feedback and observer‐type output‐feedback control protocols are designed and analyzed, respectively. By using tools from robust control theory, conditions for the existence of controllers for solving such a problem are established. It is shown that the problem of distributed H _∞ robust control synthesized with transient performance can be converted to the H _∞ control problem synthesized with transient performance for decoupled linear systems of the same low dimensions. Finally, simulation examples are provided to illustrate the effectiveness of the design. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust mixed H2/H∞ delayed state feedback control of uncertain neutral systems with time‐varying delays

This paper considers the problem of robust mixed H₂/H_∞ delayed state feedback control for a class of uncertain neutral systems with time‐varying discrete and distributed delays. Based on the Lyapunov–Krasovskii functional theory, new required sufficient conditions are established in terms of delay‐range‐dependent linear matrix inequalities for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H₂/H_∞ delayed state feedback control is derived based on a convex optimization method such that the resulting closed‐loop system is asymptotically stable and satisfies H₂ performance with a guaranteed cost and a prescribed level of H_∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Simultaneous Mixed LQR/H∞ Control Approach to the Design of Reliable Active Suspension Controllers

This paper is concerned with the synthesis of reliable controllers for quarter‐car active suspension systems. By a simultaneous mixed LQR/H_∞ control approach, a static output feedback controller is derived for guaranteeing good suspension performance under possible sensor fault or suspension component breakdown. The considered simultaneous mixed LQR/H_∞ control problem is a nonconvex optimization problem; therefore, the linear matrix inequality approach is not applicable. Based on the barrier method, we solve an auxiliary minimization problem to get an approximate solution for the simultaneous mixed LQR/H_∞ control problem. Necessary conditions for the local optimum of the auxiliary minimization problem are derived. Moreover, a three‐stage solution algorithm is developed for solving the auxiliary minimization problem. The simulation shows that the obtained static output feedback suspension controllers can improve suspension performance in nominal mode and all considered failure modes.     

Feedback stabilization of real analytic systems in the plane

We investigate the local feedback stabilization of single input control affine analytic systems in the plane. New necessary and sufficient conditions for local stabilization with feedback laws of the form u = v(x₁,x₂), x2), (v/x₁(0, 0))² + (v/x₁ (0, 0))² 0≠ 0, v(0, 0) = 0, are obtained by using Lyapunov's stability theorems on two-dimensional analytic systems. If the sufficient conditions are satisfied, we also provide explicit feedback laws.