Dissipativity of T-Periodic Linear Systems

It is proved that the existence of a positive-definite storage function is necessary and sufficient for strict dissipativity of linear systems with periodic coefficients. The connection between strict dissipativity of the system and a nonoscillatory property of an associated Hamiltonian system is established.     

Determining Dissipativity of Switched Nonlinear Systems Using Linearization

Local strict QSR‐dissipativity of a switched nonlinear system is studied using the linearization technique in this paper. We obtain local strict QSR‐dissipativity of a switched system even if each subsystem is not locally strictly QSR dissipative by designing a switching law. The derived dissipative sufficient condition is characterized by a modified Lyapunov‐Metzler inequality that can be simplified as an LMI by assuming specific forms. Two special forms of local strict QSR‐dissipativity, local input state strict passivity and local L₂‐gain, are considered. When the approximate errors of a switched affine system satisfy certain conditions, local strict passivity can be drawn from its linearization. Finally, a numerical example is given to illustrate how to apply the proposed method to achieve passivity of switched nonlinear systems.     

不确定时滞双线性广义系统的鲁棒耗散控制

针对带有耗散不确定性的时滞双线性广义系统的鲁棒耗散控制问题,首先将耗散不确定性引入双线性广义系统,利用线性矩阵不等式方法给出系统鲁棒稳定且严格耗散的充分条件;然后利用线性矩阵不等式的解,构造出闭环系统鲁棒耗散的状态反馈控制器;最后通过数值算例验证了所得结论的可行性.     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

A generalized approach to stabilization of linear interconnected time‐delay systems

The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time‐delay subsystems coupled by linear time‐varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay‐dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative state‐feedback controllers is designed to render the closed‐loop interconnected system delay‐dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Indefinite linear MPC and approximated economic MPC for nonlinear systems

The stability proof for economic model predictive control (MPC) relies on strict dissipativity, which is in general hard to check. In this contribution, we will first analyze the linear quadratic case with possibly indefinite cost. The conditions for stability will be recalled and it will be shown that every stabilizing LQR/MPC has an equivalent positive definite LQR/MPC which yields the same open loop and closed loop behavior. This analysis will then be used to formulate an approximated nonlinear economic MPC scheme, which has stability guarantees. An example will be used to illustrate the proposed technique and show its potential in terms of performance.     

Markov跳变系统的非同步事件触发耗散容错控制

本文主要研究一类具有执行器故障的Markov跳变系统的非同步事件触发耗散容错控制问题.通过引入非同步事件触发器来降低传感器的采样数据传输频率,从而降低通信消耗.采用两个独立的隐Markov模型分别描述触发器、控制器与原系统之间的非同步现象.在此框架下,基于Lyapunov稳定性和耗散理论,得到了闭环控制系统在执行器存在故障的情况下随机稳定并严格耗散的充分条件.并借助矩阵不等式变换技术给出了触发器和控制器矩阵参数的求解方法,实现了触发器和控制器的协同设计.最后,通过仿真研究验证了所提出的设计方法的有效性.     

Further Results on Dissipativity Criterion for Markovian Jump Discrete-Time Neural Networks with Two Delay Components Via Discrete Wirtinger Inequality Approach

This paper is concerned with strict \((\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma \) - dissipativity and passivity analysis for discrete-time Markovian jump neural networks involving both leakage and discrete delays expressed in terms of two additive time-varying delay components. The discretized Wirtinger inequality is utilized to bound the forward difference of finite-sum term in the Lyapunov functional. By constructing a suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee the dissipativity and passivity criteria of the proposed neural networks. These conditions are presented in terms of linear matrix inequalities (LMIs), which can be efficiently solved via LMI MATLAB Toolbox. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.     

The Kalman-Yakubovich-Popov Lemma in a behavioural framework

The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality. In this paper we derive the KYP Lemma for linear systems described by higher-order differential equations. The result is an LMI in terms of the original coefficients in which the dissipativity problem is posed. Subsequently we study the connection between dissipativity and spectral factorization of polynomial matrices. This enables us to derive a new algorithm for polynomial spectral factorization in terms of an LMI in the coefficients of a polynomial matrix.     

一类不确定广义时滞系统的鲁棒耗散控制

将耗散不确定性引入到不确定广义系统中,在状态空间下,通过线性矩阵不等式(LMI)的方法,研究了一类不确定广义时滞系统的鲁棒耗散控制问题.给出了此类不确定广义系统严格耗散的充分条件,然后设计了此类不确定广义系统的鲁棒耗散控制器,最后通过数值算例验证了定理的可行性.     

Dissipativity-based robust reduced-order fault estimation observer design of multi-agent systems

In this paper, a distributed reduced-order fault estimation observer is studied for both continuous- and discrete-time multi-agent systems with directed communication topologies. Initially, a distributed reduced-order observer is proposed to estimate the occurred faults, which can reduce the number of the fault estimation observer’s order of multi-agent systems. What is more, based on strict dissipativity and pole placement constrains, a multi-constrained design is given to calculate gain matrices of distributed reduced-order observer. Finally, simulation results are presented to demonstrate the effectiveness of the proposed distributed reduced-order fault estimation technique.     

Implications of dissipativity,inverse optimal control,and stability margins for nonlinear stochastic feedback regulators

In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton‐Jacobi‐Bellman controllers that minimize a nonlinear‐nonquadratic performance criterion with cross‐weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity, we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for stochastic dynamical systems. In particular, using extended Kalman‐Yakubovich‐Popov conditions characterizing stochastic dissipativity, we show that our optimal feedback control law satisfies a return difference inequality predicated on the infinitesimal generator of a controlled Markov diffusion process if and only if the controller is stochastically dissipative with respect to a specific quadratic supply rate.     

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACT

In this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.     

A dissipative dynamical systems approach to stability analysis of time delay systems

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.     

Implications of discretization on dissipativity and economic model predictive control

Economic model predictive control, where a generic cost is employed as the objective function to be minimized, has recently gained much attention in model predictive control literature. Stability proof of the resulting closed-loop system is often based on strict dissipativity of the system with respect to the objective function. In this paper, starting with a continuous-time setup, we consider the ‘discretize then optimize’ approach to solving continuous-time optimal control problems and investigate the effect of the discretization process on the closed-loop system. We show that while the continuous-time system may be strictly dissipative with respect to the objective function, it is possible that the resulting closed-loop system is unstable if the discrete-approximation of the continuous-time optimal control problem is not properly set up. We use a popular example from the economic MPC literature to illustrate our results.     

Dissipative analysis and control of state-space symmetric systems

The paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time-invariant systems with state-space symmetry. As a particular case of dissipative systems, we consider the mixed H_∞ and positive real performance criterion and we develop an explicit expression for calculating the H_∞ norm of these systems. Subsequently, an explicit parametrization of the static output feedback control gains that solve the mixed H_∞ and positive real performance problem is obtained. Numerical examples demonstrate the use and computational advantages of the proposed explicit solutions.     

The strict dissipativity synthesis problem and the rank of the coupling QDF

The problem of existence of a controlled behavior that is strictly dissipative with respect to a quadratic supply rate is studied. The relation between strictness and the rank of a suitable coupling condition that combines the dissipativity properties of the hidden behavior and the orthogonal complement of the plant behavior is analyzed.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

In this paper, the problems of exponential quasi‐(Q,S,R)‐dissipativity and practical stability analysis for a switched nonlinear system are addressed. First, the concept of exponential quasi‐(Q,S,R)‐dissipativity for switched nonlinear systems without requiring the exponential quasi‐(Q,S,R)‐dissipativity property of each subsystem is proposed. Then, we show that an exponentially quasi‐(Q,S,R)‐dissipative switched nonlinear system is practically stable. Second, this exponential quasi‐(Q,S,R)‐ dissipativity property for a switched nonlinear system is obtained by the design of a state‐dependent switching law. Third, a composite state‐dependent switching law is designed to render the feedback interconnection of switched nonlinear systems exponentially quasi‐(Q,S,R)‐dissipative. This switching law allows interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the results is verified by a numerical example.     

Global dissipativity of memristor-based complex-valued neural networks with time-varying delays

Memristor is the new model two-terminal nonlinear circuit device in electronic circuit theory. This paper deals with the problem of global dissipativity and global exponential dissipativity for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays. Sufficient global dissipativity conditions are derived from the theory of M-matrix analysis, and the globally attractive set as well as the positive invariant set is established. By constructing Lyapunov–Krasovskii functionals and using a linear matrix inequality technique, some new sufficient conditions on global dissipativity and global exponential dissipativity of MCVNNs are derived. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed theoretical results.