An observer-based control of linear systems with uncertain parameters via LMI approach

A dynamic output feedback variable structure controller for linear systems with mismatched uncertainties is studied. The proposed controller consists of nonlinear and linear parts. The linear part with full dynamics completely handles mismatched uncertainties and on the other hand, the nonlinear part is simplified as possible. By using the Lyapunov theory and linear matrix inequality method, the condition of existence of dynamic output feedback variable structure control law is derived and transformed as the feasibility problem described by linear matrix inequality, which can be solved by Matlab LMI toolbox to obtain the variable structure control for a class of system. A simulation example is given to illustrate that the analysis method and the result are valid and feasible.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

Preface Notation Part I. Introduction. Robust Decision Problems in Engineering: A linear matrix inequality approach L. El Ghaoui and S.-I. Niculescu Part II. Algorithms and Software: Mixed Semidefinite-Quadratic-Linear Programs J.-P. A. Haeberly, M. V. Nayakkankuppam and M. L. Overton Nonsmooth algorithms to solve semidefinite programs C. Lemarechal and F. Oustry sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure S.-P. Wu and S. Boyd Part III. Analysis: Parametric Lyapunov Functions for Uncertain Systems: The Multiplier Approach M. Fu and S. Dasgupta Optimization of Integral Quadratic Constraints U. Jonsson and A. Rantzer Linear Matrix Inequality Methods for Robust H2 Analysis: A Survey with Comparisons F. Paganini and E. Feron Part IV. Synthesis. Robust H2 Control K. Y. Yang, S. R. Hall and E. Feron Linear Matrix Inequality Approach to the Design of Robust H2 Filters C. E. de Souza and A. Trofino Robust Mixed Control and Linear Parameter-Varying Control with Full Block Scalings C. W. Scherer Advanced Gain-Scheduling Techniques for Uncertain Systems P. Apkarian and R. J. Adams Control Synthesis for Well-Posedness of Feedback Systems T. Iwasaki Part V. Nonconvex Problems. Alternating Projection Algorithms for Linear Matrix Inequalities Problems with Rank Constraints K. M. Grigoriadis and E. B. Beran Bilinearity and Complementarity in Robust Control M. Mesbahi, M. G. Safonov and G. P. Papavassilopoulos Part VI. Applications:Linear Controller Design for the NEC Laser Bonder via Linear Matrix Inequality Optimization J. Oishi and V. Balakrishnan Multiobjective Robust Control Toolbox for LMI-Based Control S. Dussy Multiobjective Control for Robot Telemanipulators J. P. Folcher and C. Andriot Bibliography Index.

In this paper, the observer-based control for a class of uncertain linear systems is considered. Exponential stabilizability for the system is studied and reduced-order observer is discussed. Numerical examples are given to illustrate obtained results.

We propose a congestion control algorithm and design a state feedback controller for regulating the congestion of available bit rate (ABR) traffic in asynchronous transfer mode (ATM) networks. ABR service is specified as the rate-based feedback mechanism for congestion control and provides a control signal to throttled sources from a bottleneck node in order to adjust the throttled source rates based on available capacity. Our main purposes are as follows: (1) to design a state feedback controller; (2) to place the closed-loop poles in any desired regions based on a pole placement constraint; (3) to use the LMI (linear matrix inequalities) approach for finding the optimal state feedback gain K. The simulation results show that, under pole placement and LMI approaches, our state feedback congestion controller for ABR traffic in ATM networks can possibly guarantee the system stability, provide no buffer overflow, determine the optimal source traffic rates and place the closed-loop poles in any desired regions as well.

This paper proposes a new robust FIR equalizer for discrete time systems subject to parameter uncertainties in the matrices of the system state-space model from an H ∞ perspective. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The discrete algebraic Riccati inequality (DARI) and linear matrix inequality (LMI) provide an extremely superior methodology in the H ∞ control fields. By the H ∞ and robust methods in conjunction with the bounded real lemma, the robust FIR equalizer design is transformed into a standard LMI optimization problem. An example is given to illustrate the proposed methodology.

Non-fragile observer-based controls of linear system via LMI approach

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is respectively obtained for the stability and stabilizability of the considered system. Moreover, an example with simulations is given to verify the effectiveness of our theoretical results.

The problem of fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control is investigated for a class of nonlinear systems with time-varying delay. Specifically, the considered system is approximated by a Takagi-Sugeno (T-S) fuzzy model. By using linear matrix inequality (LMI) methods, we design a fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller, which guarantees asymptotic stability and a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> index for the resulting closed-loop system. In contrast to the existing results, the gains of controller are obtained by solving a set of LMIs. The proposed method is easy to implement and can be applied to linear systems. A numerical example is provided to illustrate the effectiveness of the developed method.

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.

This paper investigates the problem of robust stability for a class of linear uncertain system with interval time-varying delay. Based on delay-central point method and by means of L-K stability theorem, integral inequality method and convex combination technique, a new delay-dependent stability criterion for the system is formulated in terms of linear matrix inequalities (LMIs). Unlike existing methods, when bounding the cross-terms that emerged from the time derivative of the L-K functional, neither superfluous free weighting matrices are introduced nor any useful terms are neglected, only using tighter integral inequalities and a very few free weighting matrices for expressing the relationship of the correlative terms, so that it can reduce the complexity both in theoretical derivation and in computation. As a result, it is effective to reduce the conservatism of the results. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

In this paper, an adaptive control scheme is proposed for the permanent magnet synchronous motor (PMSM) with uncertain parameters using an LMI approach. The adaptive control scheme is used to compensate some uncertain terms in the PMSM drive system. In this study, a novel formulation for the uncertain PMSM drive system is developed. By the formulation, the stability condition for the closed-loop uncertain PMSM drive system with the proposed controllers can be characterized in terms of some linear matrix inequalities (LMIs). The LMIs problem (LMIP) can be efficiently solved. Numerical solutions for the control gains and simulation results are provided to illustrate the design procedure and the performances. In opposition to try and error, the control gains in both speed loop and current loop can be obtained systematically by solving the corresponding LMIs. The proposed method is simple and is suitable for practical control design in motor drive.

Considers the class of discrete-time jump linear system with time-delay and polytopic uncertain parameters. The problems of delay-independent robust stability, stabilization and H/sub /spl infin// control are cast into the framework of linear matrix inequality (LMI) and thus solved by the LMI Toolbox of Matlab. By using the supplementary technique, the system with time-delay is converted into a higher dimension Markov system without time-delay, and thus can be handled as a standard jump linear system with uncertain parameters.

본 논문에서는 변수 불확실성과 필터이득 섭동을 가지는 시스템에 대한 견실비약성 H∞ 칼만형필터 설계기법을 제안한다. 필터가 존재할 충분조건과 견실비약성 H∞ 필터 설계기법을 선형행렬부등식 (LMI: Linear Matrix Inequality 접근법으로 제안하고 시스템과 필터의 불확실성을 매개변수화 선형행렬부등식(PLMI: Parameterized Linear Matrix Inequality)으로 구조화된 불확실성의 형태로 표현한 후 Lyapunov 함수를 통해 시스템의 불확실성과 더불어 필터이득섭동을 고려한 칼만형 H∞ 필터가 존재할 충분조건과 필터설계기법을 PLMI 형태로 보인다. PLMI는 무한개의 LMI의 형태로 나타나므로 완화기법(relaxation technique)을 적용하여 유한개의 LMI의 형태로 변환한 후 견실하고 최적화된 필터이득과 필터섭동범위를 계산하고, 예제와 모의실험을 통해 제시된 필터의 타당성을 검증한다.