Reduced-order Dynamic Output Feedback Research Articles

Output Feedback Control of Fuzzy Systems via Reduced-Order Approximation Technique

This article focuses on the problem of designing the reduced-order dynamic output feedback (DOF) controller for discrete-time T–S fuzzy plants. Differing from the existing methodologies, the reduced-order approximation technique is applied to simplify the pregiven high-order DOF controller. The key point is to construct a reduced-order closed-loop model to approximate the original high-order closed-loop system. First, a new error auxiliary system between the high-order closed-loop system and the reduced-order closed-loop model is obtained. The sufficient conditions to guarantee that the corresponding error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance index are developed. Then, the parameters of the desired reduced-order controller are derived by utilizing the projection lemma and the cone complementary linearization algorithm. Finally, the advantages of the proposed technique are illustrated by a series of simulation analysis.

Reduced-Order Min-Max Guaranteed Cost Control for Finite-Time Boundedness of Uncertain Linear Systems Using Output Feedback

This letter considers a problem of designing reduced-order dynamic output feedback controllers for finite-time boundedness of uncertain linear time-varying systems subjected to exogenous disturbances. Differential linear matrix inequality conditions are derived for finite-time boundedness with output feedback, such that the uncertain system simultaneously satisfies finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {L}_{2}$ </tex-math></inline-formula> gain in the presence of worst-case exogenous disturbances. The designed min-max controller minimizes an upper bound on the considered performance index, providing a guaranteed cost for disturbance attenuation performance. Finite-time bounded state feedback controller design is shown to be a special case of the proposed method. The performance efficacy and applicability of the controller designed using the proposed iterative algorithm are compared with some of the recent methods from the literature.

LMI-based consensus of linear multi-agent systems by reduced-order dynamic output feedback

This work proposes new conditions for consensus of homogeneous multi-agent systems subjected to exogenous disturbances in directed communication graphs by dynamic output feedback protocols. The agents under investigation are described as linear dynamics, and the communication network is such that each agent receives as information only the output of neighbor agents. The synchronization problem is rewritten as an output feedback stabilization without requiring the Laplacian matrix to be diagonalizable. As the main appeal, we propose new necessary and sufficient conditions for the design of dynamic output feedback controllers of arbitrary order – including static output feedback as a particular case – and sufficient Linear Matrix Inequalities (LMIs) for H∞ consensus. Numerical experiments illustrate the effectiveness of the proposed approach.

H∞ Output-Feedback Gain-Scheduled Control for Discrete-Time Linear Systems Affected by Time-Varying Parameters

This paper deals with the problem of H∞ reduced order dynamic output feedback control for discrete-time linear systems affected by time-varying parameters with polynomial dependency and norm-bounded terms. The main motivation comes from recent discretization methods for uncertain systems, that produce polynomially parameter-dependent discretized systems of arbitrary degree with norm-bounded terms. The design conditions are provided in terms of sufficient parameter-dependent LMI conditions combined with scalar searches, being capable to synthesize robust or gain-scheduled controllers. The approach is also particularized to handle the popular class of time-varying polytopic systems, having as novelty no requirement of special treatment for the output measured matrix. Numerical examples are provided to illustrate the potentialities of the approach to cope with discretized systems and the efficiency of the relaxations when compared with the existing methods for gain-scheduled or robust stabilization of polytopic time-invariant and time-varying systems.

Reduced-order dynamic output feedback control of uncertain discrete-time Markov jump linear systems

ABSTRACTThis paper deals with the problem of designing reduced-order robust dynamic output feedback controllers for discrete-time Markov jump linear systems (MJLS) with polytopic state space matrices and uncertain transition probabilities. Starting from a full order, mode-dependent and polynomially parameter-dependent dynamic output feedback controller, sufficient linear matrix inequality based conditions are provided for the existence of a robust reduced-order dynamic output feedback stabilising controller with complete, partial or none mode dependency assuring an upper bound to the or the norm of the closed-loop system. The main advantage of the proposed method when compared to the existing approaches is the fact that the dynamic controllers are exclusively expressed in terms of the decision variables of the problem. In other words, the matrices that define the controller realisation do not depend explicitly on the state space matrices associated with the modes of the MJLS. As a consequence, the method is specially suitable to handle order reduction or cluster availability constraints in the context of or dynamic output feedback control of discrete-time MJLS. Additionally, as illustrated by means of numerical examples, the proposed approach can provide less conservative results than other conditions in the literature.

Robust resilient [formula omitted] control for uncertain stochastic systems with multiple time delays via dynamic output feedback

This paper deals with the problem of robust resilient L2−L∞ control for stochastic systems with multiple time delays and norm-bounded parameter uncertainties via dynamic output feedback. Both additive and multiplicative controller gain perturbations are considered. New delay-dependent conditions of robust mean-square exponential stability are developed by applying the Lyapunov–Krasovskii functional method and introducing free-weighting matrices. Two lemmas are given for reducing high-order nonlinearities, with the aid of which sufficient conditions are presented for the solvability of the robust resilient L2−L∞ control problem. The desired controllers can be constructed through the numerical solutions of a set of linear matrix inequalities. The proposed design conditions can be employed to determine reduced-order dynamic output feedback controllers without the need to impose any extra constraints on the system parameters. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Non-fragile reduced-order dynamic output feedback control for switched systems with average dwell-time switching

ABSTRACTThis paper is concerned with the problem of non-fragile reduced-order dynamic output feedback control for both continuous- and discrete-time switched systems with average dwell-time switching. First, Lyapunov conditions for the analysis of asymptotic stability and weighted performance are presented. Then, sufficient conditions for the solvability of the problem of controller design are developed in terms of linear matrix inequalities. The design methods are suitable for general switched systems, without the need to impose extra constraints on the system matrices. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods.

Quantized Control Design for Cognitive Radio Networks Modeled as Nonlinear Semi-Markovian Jump Systems

This paper is concerned with the quantized control design problem for a class of semi-Markovian jump systems with repeated scalar nonlinearities. A semi-Markovian system of this kind has been transformed into an associated Markovian system via a supplementary variable technique and a plant transformation. A sufficient condition for associated Markovian jump systems is developed. This condition guarantees that the corresponding closed-loop systems are stochastically stable and have a prescribed $H_{\infty} $ performance. The existence conditions for full- and reduced-order dynamic output feedback controllers are proposed, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one, which can be solved efficiently with existing optimization techniques. Finally, an application to cognitive-radio systems demonstrates the efficiency of the new design method developed.

U-D factorisation of the strengthened discrete-time optimal projection equations

Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.

Reduced-order dynamic output feedback control of continuous-time T–S fuzzy systems

The problem of reduced-order dynamic output feedback control design for continuous-time Takagi–Sugeno fuzzy systems with H∞ guaranteed cost is addressed. The proposed approach is based on a line-integral fuzzy Lyapunov function with arbitrary polynomial dependence on the premise variables, allowing the membership functions, modeled as multi-simplexes, to vary arbitrarily. The controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two-stages linear matrix inequality procedure. The main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes. Examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous-time Takagi–Sugeno fuzzy systems.

State observer design and stabilization control for a class of nonlinear systems†

In this article, the design problems of full-order state observer, reduced-order state observer and dynamic output feedback stabilization control are investigated for a class of systems with nonlinear uncertainty. Inspired by Ha and Trinh (Automatica, 40, pp. 1779–1785, 2004), the nonlinear uncertainty is assumed to be a combination of a known Lipschitz nonlinear part and an unknown state-dependent part, on which there is no restriction, such as Lipschitz condition or monotonicity etc., imposed. The existence conditions and design methods of full-order and reduced-order state observers are obtained by means of linear matrix inequalities. Moreover, a dynamic output feedback control is constructively given to exponentially stabilize the closed-loop system. †This work was completed during the author's postdoctrol period in Academy of Mathematics and Systems Science, Chinese Academy of Science.

Global stabilisation for bilinear systems with time delay

Global asymptotic stabilisation is discussed for MIMO bilinear time-delay systems the free dynamics of which are Lyapunov-stable. Sufficient conditions for constructing state feedback, full-order dynamic output feedback and reduced-order dynamic output feedback controllers are established; the sufficient conditions can be delay-independent and delay-dependent as well. The basic analysis is based on the Lyapunov stability approach and the separation principle for bounded controllers.

Fixed-structure controller synthesis for systems with input nonlinearities and time delay

In this paper we consider the problem of stabilizing continuous-time linear systems containing input nonlinearities and time delays. Specifically, a fixed-order (i.e. full and reduced-order) dynamic outputfeedback control technique is developed and sufficient conditions involving a system of modified Lyapunov-Riccati equations are presented for stabilization of systems with sector-bounded input nonlinearities and state and measurement time delays.

Optimal guaranteed cost control of uncertain systems via static and dynamic output feedback

This paper is concerned with the design of robust static and dynamic output feedback controllers for a class of uncertain linear systems with norm-bounded uncertainty. The uncertainty is assumed to enter into both the state and input matrices. However, the output matrix is assumed to be free of uncertain parameters. Necessary conditions are given for the existence of a static output feedback controller that quadratically stabilizes the system and minimizes a bound on the quadratic function. Our results may be considered as an extension of the optimal output feedback LQR problem to the case of uncertain systems with norm-bounded uncertainty. The problem of full-order and reduced-order dynamic output feedback is also considered using the static output feedback results.

On Robust Parametric Dynamic Output Feedback

This paper presents a new and unified treatment of feedback control for linear multivariable time-invariant systems, using reduced-order dynamic output feedback to recover state feedback properties. A set of free design parameters are effectively exploited in achieving desirable performance tradeoffs, through solving Lyapunov-like matrix equations.

Pole placement for linear systems over Bezout domains

The problem of pole placement for linear systems over rings is considered. For a class of rings, our results show that one can construct reduced-order dynamic output feedback compensators for pole placement. Our results also provide an alternative proof of some previously known results on the problem of pole placement by state feedback for a class of reachable pairs ( F,G ) over Bezout domains.