RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

This thesis is concerned with the dissipative control and filtering problems of singular systems. Four classes of singular systems are considered: delay-free singular systems, singular systems with constant time-delay, uncertain singular systems with time-varying delay and sensor failures, and singular Markovian jump systems with actuator failures.
\nFor delay-free singular systems, the system augmentation approach is employed to study the dissipative control and filtering problems. First, the approach is used to solve the dissipative control problem by static output-feedback for standard state-space systems which are the special cases of singular systems. For a continuous-time standard state-space system, the closed-loop system is represented in an augmented system form. Based on the augmented system, a necessary and sufficient dissipativity condition is proposed, which decouples the Lyapunov matrix and controller matrix. To further separate the Lyapunov matrix and the system matrices, an equivalent condition is obtained by introducing some slack matrices. Then, a necessary and sufficient condition for the existence of a static output-feedback controller is proposed, and an iterative algorithm is given to solve the condition. For discrete-time singular systems, by giving an equivalent representation of the solution set, a necessary and sufficient dissipativity condition is proposed in terms of strict linear matrix inequality (LMI) which can be easily solved by standard commercial software. Then a state-feedback controller design method is given based on the augmentation system approach. The method is extended to the static output-feedback control problem and the reduced-order dissipative filtering problem.
\nFor continuous-time singular time-delay systems, the problem of state-feedback dissipative control is considered. An improved delay-dependent dissipativity condition in terms of LMIs is established by employing the delay-partitioning technique, which guarantees a singular system to be admissible and dissipative. Based on this, a delay-dependent sufficient condition for the existence of a state-feedback controller is proposed to guarantee the admissibility and dissipativity of the closed-loop system. In addition to delay-dependence, the obtained results are also dependent on the level of dissipativity. Moreover, the results obtained unify existing results on H∞ performance analysis and passivity analysis for singular systems.
\nFor discrete-time singular systems with polytopic uncertainties, time-varying delay and sensor failures, the problem of robust reliable dissipative filtering is considered. The filter is designed by the reciprocally convex approach such that the filtering error singular system is admissible and strictly (Q, S, R)-dissipative. For singular systems with time-varying delay and sensor failures, a sufficient condition of reliable dissipative analysis is obtained in terms of LMIs. Then the result is extended to the uncertain case by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, a desired filter for uncertain singular systems with time-varying delay and sensor failures is obtained by solving a set of LMIs.
\nFor continuous-time singular Markovian jump systems with actuator failures, the problem of reliable dissipative control is addressed. Attention is focused on the state-feedback controller design method such that the closed-loop system is admissible and strictly (Q, S, R)-dissipative. A sufficient condition is obtained in terms of strict LMIs. Moreover, the results obtained unify existing results on H∞control and passive control on singular Markovian jump systems.

formula omitted] model reduction for uncertain switched linear discrete-time systems

This paper is concerned with the problem of finite frequency (FF) H ∞ filter design for linear time-invariant discrete-time systems with polytopic uncertainties. Our aim is to design a new filter guaranteeing an H ∞ performance bound in a FF ranges. The H ∞ filter in designed to deal with noises in Low Frequency (LF) domain. By utilizing the Generalized Kalman-Yakubovich-Popov (GKYP) lemma, projection lemma, and we introduce many slack matrices, the conditions on the existence of H ∞ filters for LF range is unified in terms of solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed method in comparison with the existing methods.

A new looped-functional for stability analysis of the linear impulsive system

In this technical note, the problem of designing fixed-order robust $H_{infty}$ controllers is considered for linear systems affected by polytopic uncertainty. A polynomial method is employed to design a fixed-order controller that guarantees that all the closed-loop poles reside within a given region of the complex plane. In order to utilize the freedom of the controller design, an $H_{infty}$ performance specification is also enforced by using the equivalence between robust stability and $H_{infty}$ norm constraint. The design problem is formulated as a linear matrix inequality (LMI) constraint whose decision variables are controller parameters. An illustrative example demonstrates the feasibility of the proposed design methods.

This paper develops a multiple fixed model blending based adaptive parameter identification scheme for multi-input multi-output (MIMO) systems with polytopic parameter uncertainty. The developed identification scheme is proven to be asymptotically stable for uncertain linear time-invariant MIMO systems, and is shown to provide fast adaptation for even uncertain linear time-varying (LTV) systems. Furthermore, utilizing the proposed parameter identification scheme, a linear-quadratic (LQ) optimal multiple model adaptive control (MMAC) scheme is developed for linear MIMO systems with polytopic uncertainties. The proposed MMAC scheme is applied to tracking control of uncertain lateral vehicle dynamics. A set of simulation test results are presented to verify the stability and effectiveness of the proposed MMAC scheme.

In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results.

Robust Stabilizability of Switched Linear Time-Delay Systems with Polytopic Uncertainties

For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.

This article is concerned with the problem of robust H ∞ control for a half-vehicle active suspension system with input delay. The delay is assumed to be interval time-varying delay with unknown derivative. The vehicle front sprung mass and the rear unsprung mass are assumed to be varying due to vehicle load variation and may result in parameter uncertainties being modelled by polytopic uncertainty. First of all, regarding the heave and pitch accelerations as the optimisation objectives, and suspension deflection and relative tire load constraints as the output constraints, we build the corresponding suspension systems. Then, by constructing a novel Lyapunov functional involved with the lower and upper bounds of the delay, sufficient condition for the existence of robust H ∞ controller is given to ensure robust asymptotical stability of the closed-loop system and also guarantee the constrained performance. The condition can be converted into convex optimisation problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H2, and H∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

An LMI approach to guaranteed cost control of linear uncertain time-delay systems

Robust Filtering Design for Periodic Piecewise Polytopic Systems over a Low-Frequency Range

This paper investigates the design method of full order state observer for satellite attitude control system using mixed H 2 /H ∞ optimal approach. A linear system described by state space form is introduced first to state the problem of full order state observer design. The designed observer should meet the requirement of H 2 performance and H ∞ performance so that the disturbance would influence the observer as little as possible. Thus, we convert the satellite attitude control system to the same state space form, and deduce the mixed H 2 /H ∞ approach based on linear matrix inequalities (LMIs). By solving LMIs, we can obtain the solution of corresponding convex optimization problem. Then, the observer gain can be decided. The simulation results based on satellite attitude control system show that the magnitude of observer error is 10−6 rad/s within 10000s. We can conclude that the mixed H 2 /H ∞ approach of full order state observer design is effective and the external disturbance has little influence on the observation error.