Polytopic-type Parameter Uncertainty Research Articles

Retarded state-multiplicative stochastic systems - Robust H ∞ and H 2 vertex-dependent filtering

We consider linear continuous-time retarded systems with multiplicative noise and polytopic type parameter uncertainty and we address the problems of and general filtering of these systems. These problems are solved by applying a modified version of the descriptor method that leads to a considerable reduction in the over-design associated with the ”quadratic” solution that assigns a single Lyapunov function to all the points in the uncertainty polytope. The theory is extended to the robust gain-scheduling case where on-line parameter measurement is exercised in the estimation process. Two examples are given that demonstrate the superiority of our solution method. The first example relates to a simple second order system whereas the second example is one of altitude estimation taken from the field of aerospace engineering.

Mean square state estimation for sensor networks

This paper deals with mean square state estimation over sensor networks with a fixed topology. Attention is focused on designing local stationary state estimators with a general structure while accounting for the network communication topology. Two estimator design approaches are proposed. One is based on the observability Gramian, and the other on the controllability Gramian. The computation of the estimator state-space matrices is recast as off-line convex optimization problems and requires the system asymptotic stability and global knowledge of the network topology. Convergence of the estimation error variance is ensured at each network node and a guaranteed performance in the mean square sense is achieved. The proposed approaches are also extended for designing robust filters to handle polytopic-type parameter uncertainty.

Stability of adaptive control in the presence of input disturbances and H∞. performance

Adaptive control in the presence of input disturbances is considered. It is shown that standard adaptive control algorithms can stabilize the system in the presence of input disturbances and guarantee an ℒ2-gain bound. This method allows one to guarantee the performance of the adaptive control even before the adaptive parameters converge to their optimal values. The results are obtained for linear systems with polytopic type parameter uncertainties. Static output-feedback as well as state feedback are considered. The computational efficiency of the results is also discussed. An illustrative example is given.

Robust stability and control of uncertain linear discrete-time periodic systems with time-delay

This paper deals with the problems of robust stability analysis and robust control of linear discrete-time periodic systems with a delayed state and subject to polytopic-type parameter uncertainty in the state-space matrices. A robust stability criterion independent of the time-delay length as well as a delay-dependent criterion is proposed, where the former applies to the case of a constant time-delay and the latter allows for a time-varying delay lying in a given interval. The developed robust stability criteria are based on affinely uncertainty-dependent Lyapunov–Krasovskii functionals and are given in terms of linear matrix inequalities. These stability conditions are then applied to solve the problems of robust stabilization and robust H∞ control via static periodic state feedback. Numerical examples illustrate the potentials of the proposed robust stability and control methods.

Robust State-Dependent Switching of Linear Systems With Dwell Time

A state-dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed. Sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each subsystem such that it is non-increasing at the switching instants. During the dwell time, this function varies piecewise linearly in time. After the dwell, the system switches if the switching results in a decrease in the value of the LF. The method proposed is also applicable to robust stabilization via state-feedback. It is further extended to guarantee a bound on the L2-gain of the switching system; it is also used in deriving state-feedback control law that robustly achieves a prescribed L2 -gain bound.

Intermittent Fault Detection for Uncertain Networked Systems

This paper investigates intermittent fault detection problem for a class of networked systems with multiple state delays and unknown input. Polytopic-type parameter uncertainty in the state-space model matrices is considered. A novel measurement model is employed to account for both the random measurement delays and the stochastic data missing (package dropout) phenomenon, which are typically resulted from the limited capacity of the communication networks. We aim to design an uncertainty-dependent fault detection filter such that, for all unknown input, all possible parameter uncertainties, and all incomplete measurements, the error between residual and weighted fault is made as small as possible. By converting the addressed robust fault detection problem into an alternative robustH∞filtering problem of a certain Markovian jumping system (MJS), a sufficient condition for the existence of the desired robust fault detection filter is derived. A residual evaluation within an incremental form is brought forward to make the whole method suitable for intermittent fault detection. A numerical example is utilized to demonstrate the effectiveness of the proposed approach.

Robust stability and controller synthesis of discrete linear switched systems with dwell time

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l 2-gain analysis where a bounded real lemma is derived, and to H ∞ control and estimation, both for the nominal and the uncertain cases.

Robust Stability and l2–-gain Analysis of Linear Discrete-time Switched Systems with Dwell Time

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2–-gain analysis where a bounded real lemma is derived.

Robust Stability and Stabilization of Linear Switched Systems With Dwell Time

Sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, which is non-increasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs. It becomes time invariant afterwards. This function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties. The method proposed is then applied to stabilization via state-feedback both for the nominal and the uncertain cases.

Robust simple adaptive model following for linear time-delay systems with guaranteed H performance

An output-feedback model-following problem is solved, for linear time-varying delay systems with polytopic type parameter uncertainties and disturbances, using a simple direct adaptive control scheme with an additional proportional gain term which is applied to the tracking error. The objective is to obtain sufficient conditions for closed-loop stability and guaranteed H∞ performance of the proposed adaptive control scheme, so that the system output follows the output of the model. Sufficient conditions for closed-loop stability, model following performance and prescribed H∞ disturbance attenuation level of the proposed simple adaptive control scheme are given, in terms of bilinear matrix inequalities. Stability is analyzed using the Lyapunov-Krasovskii functional method, and both delay-dependent and delayindependent results are obtained. The proposed controller does not utilize the knowledge of the delay; only the bounds on the delay and the delay-rate are used. Numerical examples are given, which demonstrate the effectiveness of the proposed controller and the simplicity of its implementation.

Stability of Linear Discrete-Time Periodic Systems with Time-Delay

This paper deals with the problem of asymptotic stability of linear discrete-time periodic systems with a delayed state. A stability criterion independent of the time-delay length as well as a delay-dependent criterion are proposed, where the former applies to the case of a constant time-delay and the latter allows for a time-varying delay lying in a given interval. The developed stability criteria builds on Lyapunov-Krasovskii functionals and are given in terms of linear matrix inequalities. Extensions of the stability results for periodic systems with polytopic-type parameter uncertainty in the state-space matrices are also derived using parameter-dependent Lyapunov-Krasovskii functionals.

Robust Simple Adaptive Control for Delayed Measurements Systems

Abstract In this paper an output-feedback problem is solved for a class of linear time delayed measurements systems with polytopic-type parameter uncertainties. The objective is to make the system output follow the output of a system model. The time-delay is either constant (known) or time-varying. In both cases, the problem is tackled by applying a combination of a simple direct adaptive control scheme, a Smith-predictor, and a low-pass filter. Sufficient conditions for closed-loop stability of the proposed control scheme are given, in terms of bilinear matrix inequalities. Two numerical examples are given, which demonstrate the applicability of the proposed methods and the simplicity of their implementation.

Robust Filtering for Linear Polytopic Discrete-Time Periodic Systems

This paper is concerned with the problems of robust H∞ and guaranteed variance filtering for linear discrete-time periodic systems with polytopic-type parameter uncertainty in the matrices of the system state-space model. Filtering methods are derived for designing linear periodic asymptotically stable filters with either a prescribed upper-bound on the l2-gain from the noise signals to the estimation error, in the H∞ case, or a guaranteed upper-bound on the average steady-state variance of the estimation error variance, for the guaranteed variance filtering, in spite of the parameter uncertainty. The proposed methods are based on parameter-dependent Lyapunov functions and are given in terms of linear matrix inequalities. The potentials of the proposed filtering methods are demonstrated by an example.

Robust [formula omitted] control of continuous-time Markov jump linear systems

This paper is concerned with the problem of designing robust H 2 state-feedback controllers for continuous-time Markov jump linear systems subject to polytopic-type parameter uncertainty. Based on the parameter-dependent Lyapunov function approach, a new method for designing robust H 2 controllers is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed design method.

Robust [formula omitted] output-feedback control of systems with time-delay

The problem of designing robust dynamic output-feedback controllers for linear, continuous, time-invariant systems with uncertain time-delay in the measured output and/or the control input and with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state–space model of the system is described which permits reconstruction of its states. The resulting retarded model incorporates the uncertain parameters of the transfer function matrix in the state–space matrices and the uncertain time-delay that occurs in the control channel. To this model, the recent theory of robust H ∞ state-feedback control for retarded systems is applied. The theory is used to solve a benchmark problem of distillation column robust control design.

Robust Stability of a Class of Uncertain Markov Jump Nonlinear Systems

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result

Robust Stability and Stabilization of Uncertain Discrete-Time Markovian Jump Linear Systems

This note deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the derived results.

Robust [formula omitted] output-feedback control of linear discrete-time systems

The problem of designing H ∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H ∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.

Region-specific gene expression of Shc and Shc-related adaptor molecules

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2–-gain analysis where a bounded real lemma is derived.