Quadratic and H∞ switching control for discrete-time linear systems with multiplicative noises

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H_∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H_∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples.     

Gain‐Scheduled Control via Switching of LTI Controllers and State Reset

This paper proposes a synthesis method of gain‐scheduled control systems that switch linear time‐invariant controllers according to hysteresis of the scheduling parameter. Stability and L₂‐gain analysis and synthesis methods for switched systems are applied to the switched gain‐scheduled control synthesis using reset of the controller state, where also the reset law is computed via linear matrix inequalities (LMIs). In addition to optimization of an upper bound of L₂‐gain, we reduce jumps of control input via an auxiliary optimization. Numerical examples are presented to illustrate the switched gain‐scheduled controller.     

Asynchronous fault detection filter design approach for discrete‐time switched linear systems

This paper is concerned with the problem of the fault detection filter design for discrete‐time switched linear systems with average dwell‐time. The designed fault detection filters are also switched systems, which are assumed to be asynchronously switched with the original switched systems. Improved results on the weighted l₂ performance and the H _? performance are first given, and the multiple Lyaounov‐like functions during matched period and unmatched period for the running time of one subsystem are used. By the aid of multiple Lyapunov‐like functions combined with Projection Lemma, the FD filters are designed such that the augmented systems under asynchronous switching are exponentially stable, and the residual signal generated by the filters achieves the weighted l₂‐gain for disturbances and guarantees the H _? performance for faults. Sufficient conditions are formulated by linear matrix inequalities, and the filter gains are characterized in terms of the solution of a convex optimization problem. Finally, examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2012 John Wiley & Sons, Ltd.     

一类不确定切换奇异系统的动态输出反馈鲁棒H∞控制

研究一类由任意有限多个不确定子系统组成的切换奇异系统的动态输出反馈鲁棒H∞控制问题. 利用共同 Lyapunov 函数方法和凸组合技术, 给出由矩阵不等式表示的控制器存在的充分条件, 并设计了相应的子控制器和切换策略. 采用消元法, 将该矩阵不等式转化为一组线性矩阵不等式 (LMIs). 最后, 数值实例验证了所提方法的有效性.     

Observer-based H∞ resilient control for a class of switched LPV systems and its application

This paper deals with the issue of observer-based H_∞ resilient control for a class of switched linear parameter-varying (LPV) systems by utilising a multiple parameter-dependent Lyapunov functions method. First, attention is focused upon the design of a resilient observer, an observer-based resilient controller and a parameter and estimate state-dependent switching signal, which can stabilise and achieve the disturbance attenuation for the given systems. Then, a solvability condition of the H_∞ resilient control problem is given in terms of matrix inequality for the switched LPV systems. This condition allows the H_∞ resilient control problem for each individual subsystem to be unsolvable. The observer, controller, and switching signal are explicitly computed by solving linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed control scheme is illustrated by its application to a turbofan engine, which can hardly be handled by the existing approaches.     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.     

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ?₂-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.     

Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay

In this paper, the problem of finite‐time H _∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H _∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H _∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H _∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H _∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.     

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

This paper aims to investigate the problem of H_∞ output tracking control for a class of switched linear parameter‐varying (LPV) systems. A sufficient condition ensuring the H_∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode‐dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter‐dependent Lyapunov functions to enhance control design flexibility. Even though the H_∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H_∞ speed adjustment problem of an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability and robust H∞ control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model

This paper deals with stability and robust H_∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H_∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.     

Multiple Lyapunov Functions with Blending for Induced L2‐norm Control of Switched LPV Systems and its Application to an F‐16 Aircraft Model

This paper studies the induced L₂‐norm problem for switched linear parameter varying (LPV) systems using a blending method. For a switched LPV system where the parameters are grouped into slow‐varying and fast‐varying parameters, the blending method is used to construct blended Lyapunov functions based on the multiple Lyapunov functions conditions in terms of linear matrix inequalities (LMIs). The proposed method is applied to an F‐16 aircraft longitudinal model and the simulation results demonstrate the effectiveness of the approach.     

H∞ control of a class of 2-D continuous switched delayed systems via state-dependent switching

This paper addresses the problem of state feedback H_∞ stabilisation of 2-D (two-dimensional) continuous switched state delayed systems represented by the Roesser model using the multiple Lyapunov functional approach. First, an asymptotical stability condition of 2-D continuous switched systems with state-dependent switching is derived. Second, a sufficient condition for H_∞ performance of the underlying system is established. Third, a state feedback controller is proposed to ensure that the resulting closed-loop system has a prescribed H_∞ performance level under a state-dependent switching signal. All the results are developed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the validity and effectiveness of the proposed method.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H _∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H _∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler’s lemma and Dualization lemma, some novel conditions for exponential H _∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.     

Improved results on observer-based control for discrete-time fuzzy systems

This paper is concerned with the design problem of observer-based H_∞ control for discrete-time Takagi?Sugeno (T?S) fuzzy systems. New sufficient conditions guaranteeing the H_∞ performance of the T?S fuzzy systems are derived. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved using a single-step resolution procedure. In comparison with the existing literature results, the proposed approach may provide more relaxed conditions while ensuring better H_∞ performance. Finally, both numerical and practical examples are given to verify the effectiveness of the proposed approach.     

Switched state-feedback control for continuous time-varying polytopic systems

This article deals with switched state-feedback ?₂ control design of continuous time-varying polytopic systems. More specifically, the main goal is to determine, simultaneously, a set of state-feedback gains and a switching rule to orchestrate them, rendering the closed-loop system globally asymptotically stable for all time-varying uncertain parameter under consideration and assuring a guaranteed ?₂ cost. A contribution of the present switched control technique compared to the gain scheduling, widely used in the literature, is that the online measurement of the uncertain parameter is not required and no assumption on its time derivative is imposed. The conditions are based on modified Lyapunov–Metzler inequalities and can be solved by line search coupled with LMIs. An academic example illustrates the theoretical results and compares the present technique with other techniques from literature.     

Robust Stabilization and Tracking Control for a Class of Switched Nonlinear Systems

This paper addresses the problem of robust stabilization and tracking control for a class of switched nonlinear systems via the multiple Lyapunov functions (MLFs) approach. First, a state feedback controller and a state dependent switching law are designed to globally asymptotically stabilize the switched system via linear matrix inequalities (LMIs). The main objective of this paper is to develop a tracking control approach that assures global asymptotic output and state tracking with zero tracking error in the steady state. Then, the tracking control is formulated such that the robust H_∞ tracking performance is achieved. Finally, a simulation example is provided to demonstrate the effectiveness of the main method.     

H ∞ control of networked control systems based on event-time-driven model

This article considers the H _∞ control problem for a class of networked control systems (NCSs) based on the event-time-driven model, under which the considered NCS can be changed into a class of switched delay systems including an unstable subsystem. The Lyapunov functional exponential estimation method is adopted to solve the problem of H _∞ control for such systems. The switching controller is designed to make the considered system exponentially stable with an H _∞ norm bound in terms of linear matrix inequalities. The obtained results are less conservative than existing ones. Finally, one example is given to illustrate the effectiveness and benefit of the proposed method.     

Design on H ∞-filtering for discrete-time switched delay systems

This article is concerned with the delay-dependent H _∞-filtering problem for discrete-time switched systems with a state delay. By using the switched Lyapunov functional method and choosing a new Lyapunov–Krasovskii functional, and, furthermore, utilising the linearisation technique, sufficient conditions on the existence of a desired filter are formulated as strict linear matrix inequalities. Neither model transformation nor the bounding technique for cross-terms is involved. A numerical example is provided to illustrate the effectiveness of the proposed method.     

Discrete robust switched H∞ tracking state feedback controllers for lateral vehicle control

This paper considers the robust stability, stabilization and L₂-gain analysis of switched linear systems in the simultaneous presence of uncertain and exogenous disturbances inside subsystems. The control synthesis is performed by means of linear matrix inequalities (LMIs). The effectiveness of the proposed methods is tested and shown through lateral vehicle control application. Indeed, the simulation tests are conducted using experimental data previously recorded on a race track by an instrumented vehicle during several trials. Moreover, the stability of controlled and uncontrolled vehicle models is established by means of sideslip phase-plane criteria.     

Asynchronous Switching Control for Continuous-time Switched Linear Systems with Output-feedback

This paper investigates the asynchronous switching control problem for continuous-time switched linear systems via dynamic output-feedback, where the dynamic output-feedback controller contains an impulsive reset law to reset the controller state. A time-varying multiple Lyapunov-like-function (MLF) approach is employed to analyze the stability and weighted L₂-gain of the closed-loop systems. The switching stability criteria for the closed-loop systems are established in terms of linear matrix inequalities (LMIs), which are dependent on the upper and lower bounds of the switching interval and the asynchronous delays. The switching logic is designed to guarantee the closed-loop systems achieving the weighted L₂-gain performance. Two numerical examples are provided to show the effectiveness of the proposed method.