A General Approach to Robust Controller Analysis and Synthesis

This paper investigates the robust stability analysis and control synthesis of discrete-time switched systems with norm-bounded uncertainty under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, the equivalence between the existence of a switched Lyapunov function and two different matrix inequalities is established. These two matrix inequality conditions can be further proven to be equivalent to two LMI-based conditions. Then, some LMI-based conditions for stabilization via switched static state feedback as well as switched static output feedback are presented. In the case of state feedback, the conditions are necessary and sufficient, whereas for output feedback, the conditions are only sufficient as they depend on particular state-space representation used to describe the switched systems.

This paper considers two topics in the area of robust control system analysis and synthesis. The first topic is concerned with the testing for zero inclusion of 2-D convex polytopes, which is essential in the robustness analysis of linear systems based on generalisations of Kharitonov's four-polynomial concept. Barmish (1989) has extended the Kharitonov approach to the more general case of polynomials subject to linearly dependent coefficient perturbations and more general zero location regions, but this is accompanied by various computational problems. These are analysed and two new more direct and computationally less intensive approaches, which produce much more accurate results, are presented. The second topic is concerned with a modification to existing dyadic and full-rank pole assignment design methods for MIMO uncertain systems having affine linear perturbation structures, in which a gain factor is introduced in order to ensure robustness stability and performance. An illustrative example is also included.

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

A Reduced Order Model and a Robust Controller's Synthesis of a Black-Liquor Evaporatlon System

Modeling Approaches and Robust Stability Conditions for Networked Controlled Systems with Uncertain Delays

On the structure of generalized plant convexifying static [formula omitted] control problems

Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays

Automated Synthesis of Fixed Structure QFT Controller using Interval Constraint Satisfaction Techniques

Robust PID controller synthesis for plants with unknown or slowly varying parameters is still an open topic. A novel method is presented allowing to exactly determine all stabilizing controller gains for systems with interval and affine parametric uncertainties. This leads to far less conservative stability areas, compared to existing methods which are based on over-bounding by interval polynomials. As a consequence, iterative searches containing robust synthesis and analysis are omitted, which greatly reduces the time and effort to find potential controller parameters as robust stability is already guaranteed. Additionally, due to the inherent decoupling at singular frequencies, no frequency grinding is needed. The proposed method is based on a combination of a modified Parameter Space Approach with results from robust test set theory.

This paper presents a robust control synthesis method for linear time-invariant (LTI) differential systems with parametric uncertainty. The uncertain dynamics is described by a parametric kernel representation. We use parametric quadratic differential forms (QDF) to represent the dissipativity properties (both storage function and supply rate) of the uncertain system. The control design utilizes sum-of-squares (SOS) programming to search for a QDF supply rate for the controller such that the supply rate of the closed-loop system satisfies robust stability and performance conditions. Such a supply rate is then applied for control synthesis based J-factorization.

This paper studies the dissipative control problems for the non‐linear descriptor system via a Takagi–Sugeno descriptor model with time delay and uncertainties. The considered systems are not necessarily regular or impulse free. Using the free‐weighting‐matrix approach combined with the developed linear matrix inequality techniques, the authors proposed an improved delay‐dependent stability criterion to guarantee the system to be admissible. Based on this criterion, the solvable conditions for the existence of dissipative controller are derived, which guarantees that the closed‐loop system is not only admissible but also strictly dissipative for all admissible uncertainties. The proposed method is more suitable for the robust stability analysis and control synthesis. Moreover, different control processes can be achieved for the targeted systems in the same design process. Therefore it could potentially reduce cost and time in the controller design for an actual physical system. The authors perform simulations to validate the obtained method for practical examples.

This paper proposes a unified robust motion controller for the position and force control problems of compliant robot manipulators driven by Series Elastic Actuators (SEAs). It is shown that the dynamic model of the compliant robot includes not only matched but also mismatched disturbances that act on the system through a different channel from the control input. To tackle this complex robust control problem, the unified robust motion controller is synthesised by employing a second-order Disturbance Observer (DOb), which allows us to estimate not only disturbances but also their first and second order derivatives, and a novel controller design approach in state space. By using the Brunovsky canonical form transformation and the estimations of disturbances and their first and second order derivatives, the dynamic model of the robot is reconstructed so that a new system model that includes only matched disturbances is obtained for compliant robots driven by SEAs. The robust position and force controllers are simply designed by eliminating the matched disturbances of the reconstructed system model via the conventional DOb-based robust control method. The stability and performance of the proposed robust motion controllers are verified by simulations.

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

This paper addresses robust control design problem for parameter dependent (PD) systems subject to actuator saturation. The dead-zone nonlinearity is considered for regional stability and performance analysis of control design strategy. The parallel distributed compensation static output feedback controller is derived in new gain-scheduling scheme satisfied the generalized sector condition. Based on the fuzzy Lyapunov function approach, the parametrized stabilization non-convex conditions are reformulated in linear matrix inequalities (LMI) by congruence transformations. The proposed method leads to less conservative constraint on saturated PD controller synthesis. The effectiveness of the design methodology is demonstrated through simulations.

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >