Passivity and Passification of Uncertain Fuzzy Systems with Impulse

The passivity and feedback passification problems of fuzzy systems with parameter uncertainties and impulse are first presented in this paper. Based on the parallel distributed compensation （PDC） technique, some passivity and passification conditions are proposed in terms of linear matrix inequalities （LMIs）. Numerical examples are given to show the correctness and effectiveness of our theoretical results.     

Passivity Analysis and Passification of Markovian Jump Systems

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov–Krasovskii function and employing the free-weighting matrix technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.     

Output Feedback Passification of Switched Continuous-Time Linear Systems Subject to Saturating Actuators

This paper is concerned with the output feedback passification of switched continuous-time linear systems with actuation saturation. A switching law and saturated output feedback controllers with the form of quasi-linear parameter-varying are designed such that the closed-loop switched system with actuator saturation is passive, and the system state remains inside an invariant ellipsoid, which meet the requirements of passivity and saturation simultaneously. Since the system state is often unavailable, we consider the issue of how to design dynamic output feedback controllers using only partial state measurements. Moreover, the switching law is designed to depend only on the state of the dynamic output feedback controllers, which renders the switched system passivity even the subsystems are non-feedback passive. Sufficient conditions for the existence of the switching and output feedback control law are derived in terms of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed method.     

Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay

This paper is concerned with passivity analysis and passivity-based controller design for uncertain singularly perturbed Markovian jump systems with time-varying delay in an interval. Firstly, a delay-dependent condition for the considered system to be mean-square exponentially stable and robustly passive is derived in terms of linear matrix inequality. Then, the passification problem is investigated. Based on the obtained passivity condition, the existence of the desired state feedback controller is established. Numerical examples are presented to show the effectiveness of the proposed method.     

Finite-Time Passivity and Passification for Stochastic Time-Delayed Markovian Switching Systems with Partly Known Transition Rates

Finite-time passivity and passification is assessed for stochastic time-delayed Markovian switching systems with partly known transition rates. By employing an appropriate mode-dependent Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is constructed such that the resulting closed-loop system is finite-time bounded and satisfies the given passive constraint condition. Expressed as linear matrix inequalities, some sufficient conditions for solvability of the problem are derived. Finally, an example is given to demonstrate the validity of the main results.     

Passivity analysis and passification for uncertain signalprocessing systems

The problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers, decision feedback equalizers, and digital and analog filters. Equally important is the problem of passification, where a compensator needs to be designed for a given system to become passive. This paper considers these two problems for a large class of systems that involve uncertain parameters, time delays, quantization errors, and unmodeled high-order dynamics. By characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints (IQCs), we present solutions to the problems of robust passivity analysis and robust passification. More specifically, for the analysis problem, we determine if a given uncertain system is passive for all admissible uncertainty satisfying the IQCs. Similarly, for the problem of robust passification, we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty. The solutions are given in terms of the feasibility of one or more linear matrix inequalities (LMIs), which can be solved efficiently     

Robust Output Feedback Passification of Linear Systems with Unmodeled Dynamics

For the first time it is proposed and proved that some multi-input multi-output linear systems with unmodeled dynamics can be robustly rendered strictly positive real via static output feedback. In this work, various kinds of unstructured uncertainties are considered, sufficient conditions ensuring robust feedback passification are exploited, and feasible feedback gains are calculated. This new result generalizes existing ones which only deal with exactly modeled systems. It may also play an important role in output feedback variable structure control synthesis. This work is supported partially by the National Natural Science Foundation of China under Grants 60674017 and 60736024.     

Robust Passivity and Passification for a Class of Singularly Perturbed Nonlinear Systems with Time-Varying Delays and Polytopic Uncertainties via Neural Networks

This paper investigates the problem of robust passivity and passification for a class of singularly perturbed nonlinear systems (SPNS) with time-varying delays and polytopic uncertainties via neural networks. By constructing a proper functional and the linear matrix inequalities (LMIs) technique, some novel sufficient conditions are derived to make SPNS passive. The allowable perturbation bound ξ ^? can be determined via certain algebra inequalities, and the proposed controller based on neural network will make SPNS with polytopic uncertainties passive for all ξ∈(0,ξ ^?). Finally, a numerical example is given to illustrate the theoretical results.     

Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties

This paper deals with the problem of robust stabilization for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are obtained. Moreover, the results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is satisfied, a desired robust state feedback control law can be constructed. A numerical example is provided to demonstrate the application of the proposed method.     

Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.     

Passivity Analysis of Neural Networks With Time Delay

The passivity conditions for delayed neural networks (DNNs) are considered in this paper. We firstly derive the passivity condition for DNNs without uncertainties, and then extend the result to the case with time-varying parametric uncertainties. The proposed approach is based on a Lyapunov–Krasovskii functional construction. The passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using the effective interior-point algorithm. Numerical examples are also given to demonstrate the effectiveness of the theoretical results.     

Robust state feedback $$H_\infty $$ control for uncertain 2-D continuous state delayed systems in the Roesser model

This paper is concerned with the problem of robust state feedback \(H_\infty \) stabilization for a class of uncertain two-dimensional (2-D) continuous state delayed systems. The parameter uncertainties are assumed to be norm-bounded. Firstly, a new delay-dependent sufficient condition for the robust asymptotical stability of uncertain 2-D continuous systems with state delay is developed. Secondly, a sufficient condition for \(H_\infty \) disturbance attenuation performance of the given system is derived. Thirdly, a stabilizing state feedback controller is proposed such that the resulting closed-loop system is robustly asymptotically stable and achieves a prescribed \(H_\infty \) disturbance attenuation level. All results are developed in terms of linear matrix inequalities. Finally, two examples are provided to validate the effectiveness of the proposed method.     

An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

This paper deals with the problem of optimal guaranteed cost control via memory state feedback for a class of two-dimensional (2-D) discrete shift-delayed systems in Fornasini–Marchesini (FM) second model with norm-bounded uncertainties. A new criterion for the existence of memory state feedback guaranteed cost controllers is derived, based on the linear matrix inequality (LMI) approach. Moreover, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers which minimize the upper bound of the closed-loop cost function. Illustrative examples demonstrate the merit of the proposed method in the aspect of conservativeness over a previously reported result.     

Quadratic Stabilization of Uncertain Discrete-Time Switched Systems via Output Feedback

Quadratic stabilization of discrete-time switched systems with norm-bounded time-varying uncertainties is studied. A robust switching rule is proposed to stabilize switched systems by using a designed switched static or dynamic output feedback controller. All the switching rules adopted are constructively designed and state dependent, and they do not rely on any uncertainties.     

Robust Positive Real Synthesis for 2D Continuous Systems via State and Output Feedback

This paper considers the problem of positive real control for uncertain twodimensional (2D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm bounded in both state and measurement output equations. The purpose is the design of controllers such that the resulting closed-loop system is asymptotically stable and strictly positive real for all admissible uncertainties. A version of the positive realness of 2D continuous systems is established. Then, sufficient conditions for the solvability of the positive real control problem via state feedback and dynamic output feedback controllers, respectively, are proposed. A linear matrix inequality approach is developed to construct the desired controllers. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.     

H∞ Finite Memory Controls for Linear Discrete-Time State-Space Models

In this brief, we propose a new type of output feedback control, called a H_infin finite memory control (HFMC), for discrete-time state-space systems. Some constraints, such as linearity, unbiasedness to the optimal state feedback control, and finite memory structure with respect to an input and an output are required in advance. Among the controls needed with these requirements, we choose the HFMC to optimize the H_infin performance criterion. The HFMC is obtained by solving the linear matrix inequality problem with a parameterization of a linear equality constraint. We show through simulation that the HFMC is more robust against uncertainties, and is faster in convergence than existing H_infin output feedback controls     

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.     

Robust Passive Control for Uncertain Time-Delay Singular Systems

This paper investigates the problem of robust passive control for singular systems which contain structure uncertainties and time delay. Three types of controllers are considered, namely, state feedback controller, observer-based state feedback controller, and dynamic output feedback controller, and the controllers are constructed such that closed-loop systems are generalized quadratically stable and passive with dissipation $eta$. Design procedures and the algorithm are given for obtaining the maximum dissipation, and at the same time, the maximum guaranteed dissipation controllers are proposed. Illustrative examples are presented to show the validity and applicability of the proposed methods.      

Non-Fragile Robust Guaranteed Cost Control of?2-D?Discrete Uncertain Systems Described by?the?General Models

The problem of non-fragile robust guaranteed cost control for a class of two-dimensional (2-D) discrete systems in the general model (GM) with norm-bound uncertainties is investigated. The purpose is to design a non-fragile state feedback controller such that the closed-loop system is asymptotically stable and the cost function value is not more than an upper bound for all admissible uncertainties. The cost function is proposed and an upper bound of the cost function is given. By using a linear matrix inequalities (LMIs) approach, a sufficient condition for the solvability of the problem is obtained. A desired non-fragile state feedback controller can be constructed by solving a set of LMIs. An example is provided to demonstrate the application of the proposed design method.