Delay-dependent decentralized H∞ filtering for uncertain interconnected systems

This article considers delay dependent decentralized H∞ filtering for a class of uncertain interconnected systems, where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H∞ filter is derived, which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Finally, the numerical simulation shows the efficiency of the main results.     

Delay-dependent passive control of linear systems with nonlinear perturbation

The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive. In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity. Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities （LMIs）. In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

Robust reliable H∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.     

Disturbance Attenuation State-Feedback Control for Uncertain Interconnected Systems

This paper studies the problem of robust H∞ control design for a class of uncertain interconnected systems via state feedback. This class of systems are described by a state space model, which contains unknown nonlinear interaction and time-varying norm-bounded parametric uncertainties in state equation. Using the Riccati-equation-based approach we design state feedback control laws, which guarantee the decentralized stability with disturbance attenuation for the interconnected uncertain systems. A simple example of an interconnected uncertain linear system is presented to illustrate the results.     

Mixed H2／H∞ Optimal Guaranteed Cost Control of Uncertain Linear Systems

The mixed H2/H∞ guaranteed cost control problem via state feedback control laws is considered in this paper for linear systems with norm-bounded parameter uncertainty. Based on the linear matrix inequality (LMI) approach, sufficient conditions are derived for the existence of guaranteed cost controllers whihc guarantee not only a prespecified H∞ disturbance attenuation level on one controlled output for all admissible parameter uncertainties, but also the worst-case H2 performance index on the other controlled output to be no more than a specified bound. Furthermore, a convex optimization problem is formulated to design an optimal H2/H∞ guaranteed cost controller.     

Distributed H∞ Consensus Problem for First-Order Multi-Agent Systems with Antagonistic Interactions and Nonconvex Constraints

This paper investigates the distributed H_∞ consensus problem for a first-order multiagent system where both cooperative and antagonistic interactions coexist. In the presence of external disturbances, a distributed control algorithm using local information is addressed and a sufficient condition to get the H_∞ control gain is obtained, which make the states of the agents in the same group converge to a common point while the inputs of each agent are constrained in the noncon...     

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality (LMI) via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.     

H 2/H ∞ control problems of backward stochastic systems

This paper is concerned with the mixed H2/H∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations（BSDEs）.The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H2/H∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H2/H∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.     

Sampled-Data H∞ Dynamic Output Feedback Controller Design for Fuzzy Markovian Jump Systems

This paper considers the issue of H_∞ dynamic output feedback controller design for T-S fuzzy Markovian jump systems under time-varying sampling with known upper bound on the sampling intervals. The main aim is to realize sampled-data fuzzy dynamic output feedback control so as to demonstrate the stochastic stability and H_∞ performance index of the closed-loop sampled-data fuzzy Markovian jump systems. Then, by making the most of the information within the sampling interval,...     

A Family of Reliable H_∞ State-Feedback Controllers for Nonlinear Systems with Strictly Redundant Actuators: the Full Information Case

1　 IntroductionInherited from state space linear H∞ control theory,a number of nonlinear H∞ solutionshave been presented in terms of various formulations.The nonlinear H∞ control problemcan be stated as follows:find a compensator,either state feedback ormore general outputfeedback such that( 1 ) the internal state of the closed-loop system is stable and( 2 ) the L2 -gain of the mapping from the exogenous input disturbance to the controlled output liketracking error or cost variables is mi…     

Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay

To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.     

Stability analysis and stabilization for discrete-time singular delay systems

Stability analysis and stabilization for discrete-time singular delay systems are addressed,respectively.Firstly,a sufficient condition for regularity,causality and stability for discrete-time singular delay systems is derived.Then,by applying the skill of matrix theory,the state feedback controller is designed to guarantee the closed-loop discrete-time singular delay systems to be regular,casual and stable.Finally,numerical examples are given to demonstrate the effectiveness of the proposed method.     

Non-fragile decentralized H∞ controller design for uncertain linear systems

Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.     

Stabilization of discrete nonlinear systems based on control Lyapunov functions

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.     

State feedback stabilization for a class of nonlinear time-delay systems via dynamic linear controllers

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.     

Robust dissipative control for time-delay stochastic jump systems

A robust dissipative control problem for a class of It?-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent (RSSWDD) and strictly (Q, S, R)-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality (LMI). And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Robust H_2/H_∞ Fuzzy Filtering for Nonlinear Stochastic Systems with Infinite Markov Jump

Robust fuzzy filterings for a class of nonlinear stochastic systems with infinite Markov jump are explored based on T-S fuzzy model approach in this paper. First of all, the exponentially mean square stable filter with a prescribed H∞ performance is designed via linear matrix inequalities(LMIs). Secondly, H2/H∞ fuzzy filtering is solved in terms of LMIs by minimizing the estimation error energy under the worst case fuzzy disturbance. The corresponding fuzzy filter parameters can be received by convex optimization algorithms. And lastly, two illustrative examples are performed to manifest the validity of the proposed methods.     

Discrete-Time Mean-Field Stochastic H_2/H_∞ Control

The finite horizon H_2/H_∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma(SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic(LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H_2/H_∞ control of meanfield type via the solvability of coupled matrix-valued equations.