Design of Robust PID Controller using Static Output Feedback framework

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

Multivariable fractional order PID controller design via LMI approach

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

An improvement on multivariable PID controller design via iterative LMI approach

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

A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers

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

Robust Static and Fixed-order Dynamic Output Feedback Control of Discrete-time Lur'e Systems

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

This paper deals with the problem of static output feedback controller design for nonlinear polynomial systems using an iterative sums of squares (SOS) approach. The proposed nonlinear feedback control scheme is developed to provide the semi-global exponential stability of the controlled system using Lyapunov theory with polynomial functions. Finally illustrative examples are given to validate the proposed approach.

SummaryThis paper presents the design of output feedback controllers for discrete‐time (DT) linear systems. New sufficient LMI conditions are derived for designing static and controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback controller is designed for a quarter‐car suspension system. Simulation results are provided to show the efficacy of the proposed design method.

This paper studies the problem of reliable Hinfin state feedback controller design for linear continuous-time systems. Actuator partial failures and actuator lock-in-place failures are simultaneously considered, and the signals in the case of certain actuators being locked in place are treated as zero-frequency disturbances, which gives an exact description for the lock-in- place failures. Based on the generalized KYP lemma in finite frequency domain, the controller design is developed in the framework of linear matrix inequality (LMI) approach, which can guarantee the asymptotic stability and Hinfin performances of the resulting closed-loop systems when all control components are operational as well as when some actuators fail. Finally, the design procedure and the effectiveness of the proposed method in comparison with the entire frequency approach by using bounded real lemma are illustrated via a numerical example of flight tracking control of an F-16 aircraft.

In the above paper, it is claimed that the necessary and sufficient conditions for the static output feedback controller of fractional order singular systems are given in terms of linear matrix inequalities(LMIs). In this note, numerical examples are presented to show that both the necessary and the sufficient conditions of Theorem 3 given in [1] are incorrect. Besides, the the example in Section 4.2 of [1] constructed to support Theorem 3 is also wrong since it does not satisfy the assumption condition KC =3D — $$ G asserted and misused by the authors of [1]. A novel and solid improvement of static output feedback controller design is presented for the closed-loop fractional order singular systems to be admissible. Numerical examples are given to illustrate the proposed approaches.

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.