Pole assignment for linear time-invariant systems by periodic memoryless output feedback

It is well known that the poles of a linear time-invariant controllable and observable system can be assigned arbitrarily by state feedback. When only the output is available, pole assignment is still possible by means of dynamic output feedback. In this paper the potential of time-varying memoryless output feedback is considered. It is shown that, up to some technical conditions, it is indeed possible to allocate the poles of a linear time-invariant discrete-time system by memoryless output feedback with periodic gains. The period of the gains is (n + 1) with n the order of the system. The power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach.     

A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems

This paper studies robust performance analysis problems of linear time-invariant systems affected by real parametric uncertainties. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is know that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further extends those preceding results and propose a unified way to obtain numerically verifiable dilated LMI conditions even in the case of rational parameter dependence. In particular, it turns out that the proposed dilated LMIs enable us to assess the robust performance via multiaffine parameter-dependent Lyapunov variables so that less conservative analysis results can be achieved. Connections among the proposed conditions and existing results are also discussed concretely. Several existing results can be viewed as particular cases of the proposed conditions.     

Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min–max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min–max problem. By finding an upper bound of the worst-case performance, the min–max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.     

Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.     

四倾转旋翼无人机无源控制与飞行实验

倾转旋翼无人机以低速悬停以及快速巡航能力得到了大量的关注,但是其变化的飞行器结构(旋翼的倾转)以及较强的非线性特性(飞行速度的大范围变化)都增大了飞行控制的难度.针对一种四倾转旋翼无人机的飞行控制问题,本文中的研究内容主要基于无源性概念,改进了互联和阻尼分配无源控制以提出此飞行器的姿态与高度控制方法.通过对于飞行器动力...     

Control of a class of patterned systems

Engineering systems are often architected to consist of a number of interconnected parts that interact in distinct patterns. Because most control design methods only provide general, unpatterned control laws, a compelling open question is how to synthesise distributed control laws that adhere to a system's interconnection pattern. This paper addresses patterned control synthesis for systems with interconnection patterns. The pattern is encoded algebraically through commuting relationships of the system's state space matrices. We show that several classic control problems are amenable to a patterned synthesis. Moreover, we show that these patterned control problems have the same solvability conditions as their unpatterned counterparts. That is, a patterned control law can be found whenever any control law can be found. Our findings suggest that patterned systems naturally admit patterned controllers.     

Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback

In this paper a parameter-dependent control problem for linear parametrically varying (LPV) systems is presented. Sufficient conditions are given that guarantee an LPV system is exponentially stable and achieves an induced L₂-norm performance objective from the disturbance to error signals. The usefulness of parameter-dependent controllers is motivated from a gain-scheduling viewpoint. The resulting synthesis problem is reformulated into a convex optimization problem, which can be solved using efficient new algorithms.     

Some issues of structure and control for linear time-invariant systems

The objective of this paper is to emphasise the role played by particular structures in the solution of some control problems. The so-called “structural approach” relies on various indicators of dynamical systems such as, for instance, finite and infinite zeros, kernel indices, …. The fundamental invariance properties of these structures under the action of some transformations groups (e.g. feedback) are at the origin of their key role. Structural solutions to “classical” control problems, such as disturbance rejection, model matching and non-interaction are now rather well known: zeros at infinity play a role in the existence of “proper” solutions, while finite (invariant) zeros allow for the characterisation of “fixed poles”, whose location in the complex plane gives answer to pole placement limitations (including stability). Among the recent contributions to this structural approach, a particular attention is here devoted to:

- “Partial” versions of some of these control problems: The control objective only concerns a finite number of (and not necessarily all) the first Markov parameters of the transfer function matrix of the controlled system (e.g. to be zero for disturbance rejection or model matching, to be diagonal for non-interaction). Some interesting new issues in the dual context of failure detection are also sketched.

- Generalised solutions: Based on proportional and derivative feedback laws, with new issues in the context of systems with variable internal structures, and also for systems with delays.

Geometric concepts, such as invariant and almost invariant subspaces, and algebraic counterparts, such as factorisations on some special rings, are intermediary tools which support the characterisations of those particular structures and which allow for a structural treatment of the considered control and/or observation problems.

The results are here presented without proof: references are given to previous published results (in most cases in books and journals which are easily available), and some simple examples are used to illustrate non-standard notions (among which systems with variable internal structure, and time domain left invertibility).

Most of the results here presented rely on long and intensive collaborations between the author and various colleagues.     

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

Identification and control of Hammerstein systems via wireless networks

This article investigates a systematic approach for the identification and control of Hammerstein systems over a physical IEEE 802.11b wireless channel. Three major factors which may affect system stability and stabilisation are concerned: wireless network-induced delays, nonlinearity and model mismatch. First the network-induced delays are characterised by an inverse Gaussian distribution model according to IEEE 802.11b protocol and a model-based compensation method is used to estimate the delayed samples. Then an inverse function of nonlinear part of the identified model is used to attenuate the influence of nonlinearity, while the model mismatch is regarded as disturbance which is then dealt with by H _∞ control approach. A sufficient condition for mean-square asymptotic stability is obtained and expressed by a set of linear matrix inequalities, enabling direct controller design. Finally, numerical simulation examples are used to confirm the efficacy of the proposed approach.     

Eigenstructure assignment in a class of second-order descriptor linear systems: A complete parametric approach

1 Introduction Second-order linear systems capture the dynamic behaviour of many natural phenomena and have found wide applications[1～4] in robotics, vibration and structure analysis etc. Many results in second- order linear systems have focused on eigenstructure assignment[5～10] as an important design method. Most of the results relating to eigenstructure assignment are derived from conventional second-order linear systems. There have been few reported results produced from eigenstructure a…     

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.     

Local identifiability of time-invariant linear systems by periodic test signals

This paper is concerned with the parameter local identifiability of dynamic systems operating in periodic regimes. The systems dealt with are time-invariant and discrete-time linear systems, with an output white gaussian disturbance. Sets of frequencies are characterized such that the parameter vector is identifiable if and only if the spectrum of the periodic test signal does not vanish over one of these sets. The analysis is developed by taking also into consideration measurement schedule sets which are scattered along the time axis.     

Further results on structural assignment of linear systems via sensor selection

The problem of assigning structural properties of a linear system through sensor selection is, for a given pair (A,B), to find an output pair (C,D) such that the resulting system (A,B,C,D) has the pre-specified structural properties, such as the finite and infinite zero structures and the invertibility properties. In this paper, by introducing the notion of infinite zero assignable sets for the pair (A,B), we establish necessary and sufficient conditions for the assignability of a given set of infinite zeros and a set of structural properties which includes the left invertibility property. In establishing these conditions, we develop a numerical algorithm for the construction of the required (C,D).     

Robust fault detection of uncertain linear systems via quasi-LMIs

A novel H_∞ deconvolution filter design method is discussed for fault detection of uncertain polytopic linear systems subject to unknown inputs. The enhancement of fault sensitivity is characterized in terms of an H_- index. By means of the Projection Lemma and Congruence Transformations, a quasi-convex LMI formulation of the design problem is obtained. The effectiveness of the filter is illustrated via a numerical example.     

An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems

Stabilization of nonlinear feedback passive systems is achieved assigning a storage function with a minimum at the desired equilibrium. For physical systems a natural candidate storage function is the difference between the stored and the supplied energies—leading to the so-called energy-balancing control, whose underlying stabilization mechanism is particularly appealing. Unfortunately, energy-balancing stabilization is stymied by the existence of pervasive dissipation, that appears in many engineering applications. To overcome the dissipation obstacle the method of Interconnection and Damping Assignment, that endows the closed-loop system with a special—port-controlled Hamiltonian—structure, has been proposed. If, as in most practical examples, the open-loop system already has this structure, and the damping is not pervasive, both methods are equivalent. In this brief note we show that the methods are also equivalent, with an alternative definition of the supplied energy, when the damping is pervasive. Instrumental for our developments is the observation that, swapping the damping terms in the classical dissipation inequality, we can establish passivity of port-controlled Hamiltonian systems with respect to some new external variables—but with the same storage function.     

Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers

This paper is concerned with the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delays both in the system state and in the mode signal. The delay in the system state may be time-varying. The delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system. We first show that the resulting closed-loop system is a time-varying delayed Markovian jump linear system with extended state space. Then a sufficient condition is proposed for the design of a controller such that the closed-loop system is stochastically stable. Finally, numerical simulation is used to illustrate the developed theory.     

线性切换容错控制系统稳定性的新判据

研究了线性切换容错控制系统的稳定性问题。利用分段李雅普诺夫函数方法,结合梅茨勒矩阵的性质和矩阵不等式的分析技巧,得到了基于李雅普诺夫—梅兹勒线性矩阵不等式判定系统稳定的新结果。设计依赖于状态的切换规则便于计算、易于检验。最后利用MATLAB工具箱得到的仿真实例验证了本结果的可行性。     

Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.