Regional eigenvalue-clustering robustness of linear uncertain multivariable output feedback PID control systems

This paper proposes a time domain approach to deal with the regional eigenvalue-clustering robustness analysis problem of linear uncertain multivariable output feedback proportional-integral-derivative (PID) control systems. The robust regional eigenvalue-clustering analysis problem of linear uncertain multivariable output feedback PID control systems is converted to the regional eigenvalue-clustering robustness analysis problem of linear uncertain singular systems with static output feedback controller. Based on some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the closed-loop singular system with both structured and mixed quadratically-coupled parameter uncertainties is regular and impulse-free, and has all its finite eigenvalues retained inside the same specified region as the nominal closed-loop singular system does. Two numerical examples are given to illustrate the application of the presented sufficient condition.     

Robust control for discrete-time singular large-scale systems with parameter uncertainty

This paper addresses the problem of robust stabilization for uncertain discrete-time singular large-scale systems with parameter uncertainties. The system under consideration is not necessarily regular. The parameter uncertainties are assumed to be time invariant, but norm-bounded. The purpose of the robust stabilization problem is to design state feedback controllers such that, for all admissible uncertainties, the closed-loop system is regular, causal and stable. In terms of strict LMIs, sufficient conditions for the solvability of the problem is presented, and the parameterization of desired state feedback controllers is also given. A numerical example is given to demonstrate the applicability of the proposed design approach.     

On direct adaptive control design for nonlinear discrete-time uncertain systems

In this paper, we develop a direct adaptive control framework for adaptive stabilization of the MIMO nonlinear uncertain systems, which can be represented as discrete-time normal form with input-to-state zero dynamics. The framework is Lyapunov-based and guarantees partial stability of the closed-loop systems, such that the adaptation of the feedback gains can stabilize the closed-loop system without the knowledge of the system parameters. In addition, our results show that the adaptive feedback laws can be characterized by Kronecker calculus. Two numerical examples are given to demonstrate the efficacy of the proposed framework.     

Robust adaptive sliding mode control for uncertain discrete-time systems with time delay

This paper focuses on robust adaptive sliding mode control for discrete-time state-delay systems with mismatched uncertainties and external disturbances. The uncertainties and disturbances are assumed to be norm-bounded but the bound is not necessarily known. Sufficient conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices proposed in He et al. (2008) [3], by which the corresponding adaptive controller is also designed to guarantee the state variables to converge into a residual set of the origin by estimating the unknown upper bound of the uncertainties and disturbances. Also, simulation results are presented to illustrate the effectiveness of the control strategy.     

Model-based event-triggered control of switched discrete-time systems

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.     

On nonlinear discrete-time systems driven by Markov chains

The behavior of a class of hybrid systems in discrete-time can be represented by nonlinear difference equations with a Markov input. The analysis of such a system usually starts by establishing the Markov property of the joint process formed by combining the system's state and input. There are, however, no complete proofs of this property. This paper aims to address this problem by presenting a complete and explicit proof that uses only fundamental measure-theoretical concepts.     

Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach

This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.     

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.     

Data-driven control of consensus tracking for discrete-time multi-agent systems

This paper investigates the consensus tracking problem of leader-follower multi-agent systems. Different from most existing works, dynamics of all the agents are assumed completely unknown, whereas some input-output data about the agents are available. It is well known from the Willems et al. Fundamental Lemma that when inputs of a linear time-invariant (LTI) system are persistently exciting, all possible trajectories of the system can be represented in terms of a finite set of measured input-output data. Building on this idea, the present paper proposes a purely data-driven distributed consensus control policy which allows all the follower agents to track the leader agent’s trajectory. It is shown that for a linear discrete-time multi-agent system, the corresponding controller can be designed to ensure the global synchronization with local data. Even if the data are corrupted by noises, the proposed approach is still applicable under certain conditions. Numerical examples corroborate the practical merits of the theoretical results.     

Distributed semistable LQR control for discrete-time dynamically coupled systems

A distributed linear-quadratic-regulator (LQR) semistability theory for discrete-time systems is developed for designing optimal semistable controllers for discrete-time coupled systems. Unlike the standard LQR control problem, a unique feature of the proposed optimal control problem is that the closed-loop generalized discrete-time semistable Lyapunov equation can admit multiple solutions. Necessary and sufficient conditions for the existence of solutions to the generalized discrete-time semistable Lyapunov equation are derived and an optimization-based design framework for distributed optimal controllers is presented.     

New results on disturbance zeros of invertible linear multivariable systems

A new results concerning the definitions of disturbance zeros via the concept of minimal order system inverses is presented in this paper. These definitions are then used to develop a new computation algorithm for locating the positions of the ‘disturbance blocking zeros’ in linear multivariable systems. Assignment of disturbance blocking zeros at desired locations in the complex plane plays an important role in rejection of all measurable or un-measurable disturbances, which may affect at the outputs in steady state. Numerical examples are given to illustrate the main results of this paper.     

Observer-based discrete-time sliding mode control for systems with unmatched uncertainties

This paper addresses an observer-based sliding mode control (SMC) approach for discrete-time systems with unmatched uncertainties. A modified sliding surface based on disturbance estimation and a sliding mode controller are designed to counteract with the unmatched disturbance. The proposed method exhibits the following three features. First, the hyperplane matrix is designed in a simple way based on the discrete-time Riccati equation. Second, a chattering-free SMC method is utilized. Third, the proposed approach retains the nominal performance of the system. The stability of the overall system is achieved and simulation results are presented to verify the effectiveness of the proposed method.     

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.     

Stochastic fault tolerant control of networked control systems

A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper. By using augmented state-space method, this class of problems can be modeled as discrete-time jump linear systems governed by finite-state Markov chains. A new switched model based on probability is proposed to research problems of reliable control when actuators become ageing or partially disabled. Using improved V-K iteration algorithm, a class of reliable controllers are designed to make systems asymptotically mean square stable under several stochastic disturbances such as random time-delay and stochastic actuator failure and the maximal redundancy degree is given through this method.     

Stability-equation method for multivariable feedback control systems with lead/lag compensators

The stability-equation method is extended to the analysis and design of multivariable control systems. The systems are first compensated by constant precompensating matrices, and then compensated by lead/lag compensators. The method can take into consideration integrity and asymptotic behaviour simultaneously. In addition, other considerations, such as high frequency alignment and low-interaction at high frequency, can be analysed. Numerical examples are given and comparisons made with other methods in the current literature.     

Observer-based quantized control for discrete-time switched systems with infinitely distributed delay

This paper studies the globally almost surely exponential stabilization of discrete-time switched systems (DSSs) with infinitely distributed delay. On account of the limitation of communication resources in the actual environment, a novel class of observer-based quantized control scheme is designed that incorporates the quantization of three kinds of signals: the measurement output, the state of observer, and the measurement output of observer. By employing S-procedure and some matrix inequality techniques, an algorithm is given to design the controller parameters. To reduce the conservativeness of the obtained results, new multiple Lyapunov–Krasovskii functionals (LKFs) with negative terms are proposed to deal with the infinitely distributed delay and mode-dependent average dwell time (MDADT) switching based on transition probability (TP) is introduced to study the stabilization of DSSs with both stable and unstable modes. It is worth highlighting that the improved stabilization conditions for DSSs can release the restriction on the length of dwell time (DT) of stable and unstable subsystems. Finally, a simulation example is presented to demonstrate the validity of the proposed method.     

Event-based reference tracking control of discrete-time nonlinear systems via delta operator method

This paper investigates the event-based tracking control for delta-sampling systems with a reference model. Takagi–Sugeno (T–S) fuzzy model is used to approximate the nonlinearity. The delta operator is used to implement the discrete-time system. The event trigger is adopted for saving the network resources and the controller forces, and its detection period is designed with the same period of the delta-sampling period. Since the measurement is delayed from the sensor to the event-trigger, the methodology of time-delay systems, called the scaled small gain theorem, is applied for the system stability analysis. The reference output tracking controller is designed to ensure the stability of the resulting system in H_∞ sense. The optimization conditions of the desired H_∞ event-based tracking controller are synthesized, and the simulation example validates its effectiveness finally.     

Sampling and control of switched linear systems

In this paper, we address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.