Dynamic output feedback control for continuous-time Markov jump linear systems with hidden Markov models

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

H2 dynamic output feedback control of phase-type semi-Markov jump linear systems

International audience

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.

This paper considers linear time-invariant control systems over fading channels in both continuous-time and discrete-time cases and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program. This condition is obtained by reformulating mean square stability as asymptotical stability of a suitable matrix comprising plant, controller, and channel, and by introducing modified Hurwitz and Schur stability criteria.

Positive real control for 2-D discrete delayed systems via output feedback controllers

This work considers the design of optimal static output feedback controllers with priori structural constraints for linear systems. The structural constraints impose individual elements of the feedback matrix to satisfy certain equality or inequality constraints. The barrier method is used to address an auxiliary minimization problem to attain an approximate solution to the original nonconvex constrained optimization problem. The Lagrange multiplier method is applied to derive necessary conditions for the optimal solution. An easy-to-implement algorithm based on the gradient descent method is developed to solve the auxiliary minimization problem, and the convergence of the algorithm is proven. The effectiveness of the proposed methodology is validated using two numerical examples.

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 is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.

Absolute stabilization of Lur’e systems via dynamic output feedback

6 - Design and Performance of Feedback Controllers

5 - Iterative schemes and convergence analysis

Rbust control of linear systems with real parametric uncertainty

This paper deals with the problem of robust fault-tolerant dynamic output feedback controllers design for time-delay systems. The system under consideration involves parameter uncertainties and time-delay. The purpose is to design the dynamic output feedback controller such that, for all admissible uncertainties as well as actuator failures, the system remains stable. The sufficient condition is given in the form of linear matrix inequalities (LMIs) to maintain the stability of the closed-loop system for the time-delay system against actuator failures, and the design of the dynamic output feedback controller is proposed. Finally, an illustrative example and simulation results are given to demonstrate the effectiveness of the proposed method.

Spectral design of output feedback controllers for systems pre-compensated by input shapers