Static output feedback controller design for fuzzy systems: An ILMI approach

An LMI-Based Approach to Static Output Feedback Stabilization of T—S Fuzzy Systems

This article considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems via 0<α<1 subject to input saturation with convex polytopic uncertainties, by a kind of [Formula: see text]–proportional–integral–derivative control synthesis. A new saturation-based stability condition is suggested to estimate the stable region ([Formula: see text]) and region of attraction (ε) using the ellipsoid approach. The main concept of the presented strategy is based on transforming the proportional–integral–derivative controller design problem into the static output feedback control problem. Gronwall–Bellman lemma and sector bounded condition of the saturation function is used for stability investigation and stabilization of such systems. The static output feedback control laws are obtained with the aid of a non-iterative linear matrix inequality implication. From the static output feedback controller, the proportional–integral–derivative controller is then restored. Stability problem is addressed as an optimization problem to obtain the controller gains and the stable region, as well as the largest region of attraction. Some theorems and numerical examples are provided to illustrate the results of proposed mechanism.

Improved stability criterion and output feedback control for discrete time-delay systems

A static output feedback model predictive control algorithm is proposed for an uncertain linear continuous system. An explicit expression for the static output feedback control law is developed in light of the projection lemma. An infinite time domain optimization problem is transformed into a linear programming problem. The solvability of the optimization problem and the stability are proved to underpin the proposed approach. The effectiveness of the proposed method is validated by using case studies.

This paper considers the problems of designing multivariable proportional-integral-derivative (PID) controllers for discrete-time systems with D-stability and/or performance constraints. First, the PID control problem is cast into a static output feedback (SOF) control problem, and linear matrix inequality (LMI) conditions are presented. Then, a cone complementarity linearisation (CCL) method is used to solve the SOF-stabilisation problem, and a coordinate transformation matrix (CTM) optimisation approach is extended to solve the optimal SOF control problem. Finally, a numerical example is provided to show the effectiveness and advantage of the CTM optimisation approach, and application to the anti-sway and positioning control of an overhead crane demonstrates the validity of the approach.

This study is concerned with the problem of observer-based output feedback control for T-S fuzzy systems with time-delay under imperfect premise matching. The objective is to design an observer-based controller such that the closed-loop control system is asymptotically stable. The proposed fuzzy controller and fuzzy observer do not need to share the same premise membership functions and number of rules with T-S fuzzy systems, which makes the controller and observer design more flexible. Using a recently developed integral inequality, a delay-dependent method for the controller and observer design is provided. With the help of some advanced matrix inequalities, the proposed conditions are presented in the form of linear matrix inequalities (LMIs). An illustrative example is given to show the effectiveness of the present result.

ROBUST H∞ STATIC OUTPUT FEEDBACK CONTROL OF FUZZY SYSTEMS: AN ILMI APPROACH

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.

Finite-time H∞ control for T–S fuzzy descriptor semi-Markov jump systems via static output feedback

This paper investigates the problem of event-triggered dissipative observer-based output feedback control for a class of Takagi-Sugeno (T-S) fuzzy singular systems with unavailable states, time-varying delays, and imprecise membership functions. The considered singular system is presented as a T-S fuzzy singular system which gives a more realistic presentation for a variety of non-linear dynamical systems than conventional state space representation. The general framework we designed is based on a fuzzy observer-based controller with time varying delay along with extended dissipativity, which provides the H∞, L2-L∞ and dissipative performance indices and is robust against the disturbances and time-varying delay. Moreover, a novel Lyapunov-Krasovskii functional is adopted to analyze the closed loop stability of the fuzzy system. The solvability of Lyapunov-Krasovskii functional results in the formation of linear matrix inequalities. The controller and observer gains can be obtained by solving the linear matrix inequalities. Simulations are performed to validate the proposed scheme.

This paper is focused on the static output feedback (SOF) control problem for a class of switched nonlinear systems with actuator faults. By means of the Takagi-Sugeno fuzzy model, the switched nonlinear plant is described by a family of switched fuzzy systems. Considering transmission failures may occur between controller and actuator, a reliable SOF controller against actuator faults is designed. Sufficient conditions are developed to guarantee the existence of the reliable SOF controller. Furthermore, an iterative algorithm is designed to determine the controller gains, which avoids the conservatism brought by the traditional singular value decomposition method. To validate the effectiveness of the proposed approach, a numerical example is exploited and simulation results are also presented.

Static output feedback control of nonhomogeneous Markovian jump systems with asynchronous time delays

Combined input–output finite-time stability condition with static output-feedback H ∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H ∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H ∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

Robust Finite Frequency ℋ∞ Passive Fault Tolerant Static Output Feedback Control with Application to Active Vibration Attenuation