Passivity analysis for uncertain signal processing 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.

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach.

The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as a connection of a known LTV system and a perturbation. The state matrices of the LTV system are assumed to be rational functions of time. This is used to model the uncertain LTV system as an connection of a time invariant system and an augmented perturbation that includes time. The input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Static and dynamic IQCs are developed for the multiplication by time. A sufficient condition to bound the induced L2 gain is formulated using dissipation inequalities and IQCs. The approach is demonstrated with two simple examples.

This paper considers a problem of absolute stabilization with a specified level of disturbance attenuation for a class of uncertain systems in which the uncertainty is structured and satisfies a certain integral quadratic constraint. The paper shows that an uncertain system is absolutely stabilizable with a specified level of disturbance attenuation if and only if there exists a solution to a corresponding H/sup /spl infin// control problem. The paper also shows that if an uncertain system can be absolutely stabilized with a specified level of disturbance attenuation via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control. A key technical result used in this paper is an extension of the S-procedure result of Megretsky and Treil (1993).

In this paper, the problem of robust performance analysis of interconnected uncertain systems with hierarchical structure is investigated. The computational load associated with such problems does not allow a direct application of robustness analysis usual tools. To overcome this difficulty, we exploit the hierarchical structure of the problem and propose an algorithm to perform robustness analysis using integral quadratic constraint “propagation” along the hierarchical structure. This algorithm allows us to establish a tradeoff between computation time required to perform the analysis and the conservatism of the obtained results. Furthermore, it is possible to perform parallel computation using the proposed algorithm.

This paper presents a new dilated linear matrix inequality (LMI) representation to design a state feedback controller and a dynamic feedforward disturbance compensator for linear parameter-varying (LPV) systems. The improved LMIs are convex and finite-dimensional without any iterative approach. The designs are based on a new proposed equivalent bounded real lemma (BRL) by means of matrix dilation for LPV systems and uncertain linear systems under time-varying parametric uncertainties (TVPUs). This dilated BRL provides lower conservative results than existing methods in terms of robust stability. Accordingly, a dynamic disturbance compensator is designed in addition to a state feedback controller. This paper mainly focuses on the design of compensators against disturbances in addition to the design of state feedback controllers. The dynamic matrices of the compensator change with the time-varying parameters of the LPV or uncertain system during operation, assuming that the disturbances and the parameters are measurable or observable. The compensator can be designed to attenuate the disturbances/noises or to improve reference tracking. Finally, numerical and simulation outcomes are presented to prove both the effectiveness and lower conservativeness of the proposed LMIs.

We consider the sliding-mode output feedback controller (SMOFC) design problem for a class of uncertain multivariable systems. We first design a stabilizing SMOFC for matched uncertain systems. Using linear matrix inequalities (LMIs), we derive a necessary and sufficient condition for the existence of a linear sliding surface depending on outputs and compensator states. Using the solution of the LMI existence condition, we characterize the gain matrices. We give the nonlinear switching feedback gain guaranteeing the reachability condition. Second, we give an LMI-based design method to combine various useful performance criteria which can be used to guarantee a desired robust performance in spite of mismatched uncertainties. The performance criteria include alpha-stability, LQ performance, H 2/H infin performance, and peak-to-peak gain bound. In particular, we show that by including H infin performance constraints, we can easily solve the SMOFC design problem for challenging system models to which the previous methods are not easily applicable. Finally, we give a numerical design example showing that our method can be successfully applied to the problem of designing reduced-order SMOFCs for uncertain time-delay systems or mismatched uncertain systems.

This paper addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm-bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMI) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the paper are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time-delay systems. Numerical examples are presented to show the effectiveness of the approach.

This paper develops a necessary and sufficient condition for the following relationship to exist between two given uncertain systems defined in terms of IQCs: Every input-output behaviour of the first uncertain system is an input-output behaviour of the second uncertain system.

H In this paper we address the problems of robust stability and robust perform2 ance for uncertain discrete time systems with nonlinear parametric uncertainties. We consider two families of systems with parametric uncertainties described by state-space models which offer a fairly general representation of most uncertain systems with one or two parameters (the approach can be extended to more parameters). For these two families we obtain explicit expressions for the Schur stability H radius and for the robust performance radius in the case of uncertainties with a 2 single parameter. Moreover, we provide a line search algorithm for these two problems in the case of two parameters. Both for the robust stability and the robust performance problem, explicit necessary and sufficient conditions are derived.

This paper focuses on uncertain pendulum-like systems subject to norm constraint structured uncertainties, and addresses the robust gradient-like behaviour analysis and synthesis problems for such systems. By applying the structured singular value of an operator to structured uncertainty, the results on robust analysis for the gradient-like behaviour of uncertain pendulum-like systems are obtained. Based on the analysis results, using KYP lemma, a dynamic output feedback controller for the closed loop system guaranteeing gradient-like behaviour is designed and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. Finally two numerical examples are presented to demonstrate the applicability and validity of the proposed approach.

The problem of guaranteed cost robust Hinf reliable control is investigated for time-delayed uncertain systems against actuator failures. In the considered system, the parameter uncertainty satisfies a generalized matching condition, and all the outputs of the actuator failures are assumed to be zero. Based on Lyapunov stability theory, a sufficient condition of the existence of guaranteed cost robust Hinf reliable controller is derived and furthermore transformed to a linear matrix inequality (LMI). At the same time, the designing approach of state feedback controller is presented and the upper bound of guaranteed cost function is given. The resultant control systems not only could retain asymptotic stability and disturbance attenuation with Hinf-norm bounds but also possess the performance index of guaranteed cost irrespective of any outages within a prespecified subset of actuators. A numerical example shows the validity of the proposed design method.

Time delay is prejudicial to power system stability and generally worsens the performance of control system. In this paper, the approaches for stability analysis and stabilization of a power system consisting of time-varying delay are established. The paper starts with modeling of the power system according to time-delay differential algebraic equations. An Integral Quadratic Constraints (IQC) method is constructed to guarantee the stability of proposed feedback controller. The frequency-domain IQC and time-domain dissipation inequality are effectively combined to perform stability analysis and stabilization of power system considering time delays, without complex numerical computation. A 2-area 4-machine system, an IEEE ten-machine thirty nine-bus system and a WECC 179-bus system are employed to support the stability criteria and IQC method. The simulation results indicate that the combined methods effectively damp the oscillation and improve the performance.

This paper proposes the sliding mode control using LMI techniques and adaptive recurrent fuzzy neural network (RFNN) for a class of uncertain nonlinear time-delay systems. First, a novel TS recurrent fuzzy neural network (TS-RFNN) is developed to provide more flexible and powerful compensation of system uncertainty. Then, the TS-RFNN based sliding model control is proposed for uncertain time-delay systems. In detail, sliding surface design is derived to cope with the non-Isidori-Bynes canonical form of dynamics, unknown delay time, and mismatched uncertainties. Based on the Lyapunov-Krasoviskii method, the asymptotic stability condition of the sliding motion is formulated into solving a Linear Matrix Inequality (LMI) problem which is independent on the time-varying delay. Furthermore, the input coupling uncertainty is also taken into our consideration. The overall controlled system achieves asymptotic stability even if considering poor modeling. The contributions include: i) asymptotic sliding surface is designed from solving a simple and legible delay-independent LMI; and ii) the TS-RFNN is more realizable (due to fewer fuzzy rules being used). Finally, simulation results demonstrate the validity of the proposed control scheme.

In this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.