Static Output Feedback Controller Design Research Articles

Synthesizing Negative-Imaginary Systems With Closed-Loop H∞-Performance Via Static Output Feedback Control

Abstract This paper develops an algorithm for synthesizing negative imaginary (NI) systems with a specified H∞-norm bound by exploiting the convex relaxation technique in the static output-feedback (SOF) control design framework. This scheme improves the robustness objective since the present framework can handle both NI and H∞-norm-bounded unstructured uncertainty of the system. The non-strict inequality involved in the NI system description that creates a major difficulty in the SOF control design, can efficiently be tackled by the developed convex relaxation-based iterative algorithm. The advantages of the algorithm are shown using several examples and the results are compared with the existing works.

Mixed H∞ and passive resilient control for discrete-time systems with Round-Robin protocol and deception attacks

This paper focuses on the mixed [Formula: see text] and passive resilient control problem for uncertain discrete-time networked control systems subject to time delays. The measurement output is considered to be quantized by the dynamic quantizer before transmission through an unreliable communication channel, where the deception attacks may occur randomly. To further reduce the communication burden, the Round-Robin (RR) protocol is adopted to schedule sensors in a predetermined transmission order. Meanwhile, a new performance index is developed to solve restriction of the same dimension of control output and the exogenous disturbance. The S-procedure combined with a two-step uncertainties elimination method is adopted to deal with the nonlinear product terms involving multiple uncertainties. Furthermore, a decoupling method is introduced for static output feedback controller design. Sufficient conditions of the resilient controller and the dynamic quantizer are provided, which can improve the robustness of resulting closed-loop system and guarantee its stochastic stability and the specified mixed [Formula: see text] and passivity performance index. Finally, an example is given to illustrate the feasibility of the theoretical results.

Robust H[formula omitted]-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation

This paper deals a type of H∞ proportional–integral–derivative (PID) control mechanism for a type of structural uncertain fractional order linear systems by convex Polytopic and two-norm bounded uncertainties subject to input saturation which mainly focuses on the case of a fractional order α such that 0<α<1. The Gronwall–Bellman lemma and the sector condition of the saturation function are investigated for system stability analysis and stabilization. The main strategy of the presented strategy is to restore fractional order PID controller design under input saturation problem from static output feedback controller design. Unlike existing strategies, non-iterative strategy is used to get optimal output feedback based on the LMI. On the premise of a linear matrix inequality algorithm, the SOF control laws can be obtained. After that, the fractional-order PID controller is recovered from the SOF controller. A numerical example is provided in order to show the validity and superiority of the proposed method.

Decentralized static output feedback controller design for linear interconnected systems

Decentralized static output feedback controller design for linear interconnected systems

Nonnegative Consensus Tracking of Networked Systems With Convergence Rate Optimization.

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies.

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.

Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems

This paper investigates the stabilization of uncertain neutral-type delay fractional systems. Both static and dynamic output feedback control design methods are proposed. A guaranteed cost-based feedback control design is considered and closed-loop robust stability is investigated using the Lyapunov theorem. Asymptotic stability conditions of the closed-loop system is described in terms of linear matrix inequalities (LMIs). A simulation study, encompassing a numerical example of a fractional order system and a two stage chemical reactor, is considered to assess the performance and validity of the proposed control design.

Stabilization of rational nonlinear discrete-time systems by state feedback and static output feedback

The design of State Feedback (SF) and Static Output Feedback (SOF) controllers for nonlinear discrete-time systems subject to time-varying parameters is discussed in the context of Difference-Algebraic Representations (DAR) and parameter-dependent Lyapunov functions applied to obtain convex conditions in the form of Linear Matrix Inequalities (LMI). The proposed conditions guarantee the system robust stabilization and provide an estimate of the Domain-of-Attraction (DoA). Firstly, a novel strategy for gain-scheduled SF control is proposed incorporating information on the system’s nonlinearities to compute the control action. Secondly, a new gain-scheduled SOF control design solution is derived, without structural constraints imposed on the output matrix and without making use of iterative algorithms, unlike most approaches in the current literature. Finally, numerical examples illustrate the proposed methodology’s potential.

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ ∞ gain‐scheduling static output feedback control

The stabilization of discrete-time linear parameter-varying (LPV) systems via gain-scheduling static output feedback (SOF) control is addressed in this article. We propose new sufficient linear matrix inequalities (LMI) conditions for synthesizing a gain-scheduled SOF controller that ensures asymptotic stability and also imposes a lower bound on the closed-loop decay rate. The SOF controller design is based on a two-step method: a state-feedback controller is obtained in a first-stage design, which is then used as input information in the second stage for computing the desired gain-scheduled SOF controller. The proposed LMI constraints are given in terms of the existence of affine parameter-dependent Lyapunov functions, considering arbitrarily fast variation of the time-varying parameters. An extension for coping with disturbance rejection is also proposed, in terms of the H ∞ $$ {\mathcal{H}}_{\infty } $$ guaranteed cost optimization. Some numerical experiments are presented to illustrate the control synthesis procedure and its efficacy. Also, feasibility analyses are presented to compare and show the advantages of our results over other available strategies present in literature.

Output feedback control for bipartite consensus of nonlinear multi-agent systems with disturbances and switching topologies

The bipartite consensus protocol for nonlinear multi-agent system (MAS) subject to switching interaction graphs and external disturbances is addressed in this paper. The coordination goal of this paper is to present a static output feedback control design such that the bipartite consensus of the considered MAS can be achieved with prescribed mixed H∞ and passive performance. We consider undirected structurally balanced signed network topologies to express the cooperative and competitive interaction between neighboring agents. To achieve the desired objective of this paper, the problem under consideration is first transformed into a stabilization problem by using the properties of Laplacian matrix. Then utilizing Lyapunov stability theory, the desired bipartite consensus conditions are developed for the resulting model in terms of linear matrix inequalities. Ultimately, a numerical example is provided to verify the robustness of the considered static output feedback control design.

L 2-based static output feedback controller design for a class of polytopic systems with actuator saturation

ABSTRACT This paper presents a robust -based Static Output Feedback (SOF) controller design for a class of linear continuous-time polytopic systems subject to actuator saturation, which is a feature common to vast industrial processes. New sufficient LMI conditions are derived for the design of SOF controllers using parameter-dependent Lyapunov function. The development incorporates the decomposition of an auxiliary matrix variable so that approximation in deducing the LMIs involve reduced-size matrices. In addition, performance under the constraint of actuator saturation is considered to develop a framework of a considerably complete problem. Several design cases are taken to demonstrate the efficacy of the proposed method. Moreover, the completeness of the design is illustrated through experimental results on a twin-rotor MIMO system, and comparison of the results is presented with those existing in the literature.

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

On LMI conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties

This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results.

Exponential stabilization for 1-D linear Itô-type state-dependent stochastic parabolic PDE systems via static output feedback

This paper deals with the problem of exponential stabilization for 1-D linear stochastic parabolic partial differential equation (PDE) systems with state-multiplicative noise in the form of Itô type. A static output feedback (SOF) control scheme is proposed to stabilize the stochastic PDE system in a stochastic framework via locally collocated piecewise uniform actuators and sensors. The closed-loop well-posedness analysis is provided by virtue of the semi-group theory. Based on the infinite-dimensional infinitesimal operator and Lyapunov technique, the SOF controller design is developed to guarantee the exponential stability of the resulting closed-loop system in the mean square sense. Finally, simulation results on a stochastic heat equation are presented to verify the effectiveness of the proposed design method.

Robust Static Output Feedback H2/H∞ Control Synthesis with Pole Placement Constraints: An LMI Approach

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.

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Stability and stabilization for LPV systems based on Lyapunov functions with non-monotonic terms

This paper presents new conditions for stability analysis, static output-feedback and state-feedback control design for discrete-time linear parameter-varying systems. The proposed methodology is based on the combination of quadratic “Lyapunov-like” terms such that individually each one is not necessarily monotonically decreasing along the state trajectories. Firstly, a new necessary and sufficient stability analysis condition based on the use of non-monotonic terms in the Lyapunov function is proposed. Concerning the stabilization problem, a novel strategy for the static output-feedback control design is proposed and, unlike most approaches in the literature, no structural constraints on the output matrix are imposed, which it is an extra feature advantage of the proposed method as well. Besides that, a new gain-scheduling state-feedback control design solution is derived. All proposed conditions are presented in the form of Linear Matrix Inequalities and their feasibility implies the existence of a Lyapunov function that is monotonically decreasing along trajectories. Numerical experiments illustrate the potential of the proposed techniques.

H∞ controller design of networked control systems with a new quantization structure

This paper is concerned with the problem of H∞ static output-feedback control for networked control systems (NCSs) with quantization and Markov packet dropouts. A new quantization structure is proposed, and a mathematical treatment of this structure is given to illustrate the advantage for the quantization effects. Moreover, two Markov chains are adopted to describe the packet dropouts, not all the elements of the transition probability matrices are assumed to be known. Then, the closed-loop systems are modeled as the Markov jump linear systems (MJLSs) with partly unknown transition probabilities. An H∞ static output-feedback controller design method is given to ensure the stability of the corresponding closed-loop systems with proposed quantization structure and satisfy the H∞ performance for the external bounded disturbance in terms of linear matrix inequalities (LMIs). A simulation example is utilized to demonstrate the effectiveness and the applicability of developed approach.

New gain‐scheduled static output feedback controller design strategy for stability and transient performance of LPV systems

In this study, a new static output feedback (SOF) control for application to linear parameter-varying (LPV) systems is proposed. The asymptotic stability of LPV systems is ensured based on the proposal of a design strategy for gain-scheduled static output feedback (GS-SOF) controllers. The approach selected for the design of the GS-SOF gains is based on a two-stage method, which consists of obtaining a state feedback gain in the first stage, and then in the second stage, using that information to derive the desired GS-SOF controller. In the controller design, the proposed strategy considers performance improvement regarding the specification of the minimum decay rate. The solution for the investigated problem is presented in terms of linear matrix inequalities (LMI) obtained using Finsler's Lemma. Less conservative LMI conditions are also proposed by considering parameter-dependent slack variables. For illustration purposes, the proposed method is implemented in practice for the design of GS-SOF controllers for an active suspension system. In the experiments, it is assumed that only one of its four system state variables is available for the measurement. The dynamic performance achieved in the practical implementation of the designed controllers demonstrates the efficiency of the method.

Finite-Frequency Fuzzy Output Feedback Controller Design for Roesser-Type Two-Dimensional Nonlinear Systems

This article studies the problem of finite-frequency static output feedback (SOF) \mathscr H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller design for discrete-time Roesser-type two-dimensional (2-D) nonlinear systems based on Takagi-Sugeno (T-S) fuzzy models. The 2-D Roesser nonlinear systems are described by T-S fuzzy models with parameter uncertainties. The objective is to design a SOF controller guaranteeing the asymptotic stability of the resulting closed-loop system with finite frequency \mathscr H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Via a system state-input augmentation technique, the closed-loop system is formulated in a descriptor form. Then, based on fuzzy Lyapunov functions and some elegant convexification procedures, the SOF controller design approach is proposed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.