Structured analysis of piecewise‐linear interconnected systems

This paper considers the problem of assessing the induced L₂ gain of a system composed of non‐identical interconnected piecewise‐linear subsystems, when the topology of the underlying graph is arbitrary. Blending tools inspired by dissipativity theory and the S‐procedure, it presents sufficient conditions in the form of a set of finite‐dimensional linear matrix inequalities which are coupled in a way that reflects the spatial structure of the system under analysis. Results are presented comparing the efficacy of the new conditions to similar conditions for an equivalent global piecewise‐linear system. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Fault detection problem for discrete-time impulsive system using mixed dissipativity approach

This article studies the fault detection problem for a class of discrete-time impulsive systems using mixed dissipativity theory. First, under the impulsive effects, a fault diagnosis observer is designed such that it is insensitive to disturbances, and sensitive to faults. Then, a mixed dissipativity concept is introduced to deal with impulsive effects, disturbances insensitivity condition and faults sensitive condition in one framework such that the impulsive error dynamic is dissipative with respect to the proposed mixed supply rate. Based on the proposed mixed supply rate, sufficient conditions are obtained to guarantee the dissipativity of the impulsive estimation error dynamic. Moreover, sufficient conditions are established for the existence of the desired fault observer. The corresponding solubility conditions for the designs of the desired observer are also obtained. Finally, simulation results are proposed to demonstrate the effectiveness of our proposed strategy.     

Output regulation control for switched stochastic delay systems with dissipative property under error-dependent switching

In this paper, the output regulation problem with dissipative property for a class of switched stochastic delay systems is investigated, based on an error-dependent switching law. Under the assumption that none subsystem is solvable for the problem, a sufficient condition is derived by structuring multiple Lyapunov–Krasovskii functionals with respect to multiple supply rates, via designing error feedback regulators. The condition is also established when dissipative property reduces to passive property. Finally, two numerical examples are given to demonstrate the feasibility and efficiency of the present method.     

Delay‐dependent dissipativity analysis and synthesis of switched delay systems

In this paper, we study the problem of dissipative analysis for a class of switched systems with time‐varying delays. Sufficient conditions for dissipativity are developed for a class of switching signals with average dwell time. These conditions express delay‐dependent exponential stability and are provided in terms of linear matrix inequalities (LMIs). It is shown that the derived results encompass some available results on ??_∞ approach and arbitrary switching case. Numerical examples are given to illustrate the developed results. Copyright © 2010 John Wiley & Sons, Ltd.     

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.     

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.     

经济性预测控制的切换控制策略优化算法设计

针对经济性预测控制优化问题,设计了切换控制策略的优化算法。首先,离线计算具有耗散性的Hessian矩阵指标;其次,在线优化阶段,根据系统状态所处的不同可行域,分别在经济指标优化和Hessian矩阵对应的动态指标优化之间进行切换,从而驱动系统状态收敛到稳态工作点,取得了较优的经济性能;最后,仿真结果验证了方法的有效性。