Stability and Stabilization of Block-cascading Switched Linear Systems

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

Robust stability analysis for a cruise missile

A global controller design methodology for a flight stage of the cruise missile is proposed. This methodology is based on the method of least squares, To prove robust stability in the full airspace with parameter disturbances, the concepts of convex polytopic models and quadratic stability are introduced, The effect of aerodynamic parameters on system performance is analyzed. The designed controller is applied to track the overloading signal of the cruise segment of the cruise missile, avoiding system disturbance owing to controller switching, Simulation results demonstrate the validity of the proposed method.

Quadratic stabilization for uncertain stochastic systems

This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems, where the uncertain matrix is norm bounded, and the external disturbance is a stocbastic process, Two kinds of controllers are designed, which include state feedback case and output feedback case. The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities. The detailed design methods are presented. Numerical examples show the effectiveness of our results.

LMI conditions for quadratic and robust D-stability of interval systems

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

Robust Input-Output Energy Decoupling for Uncertain Singular Systems

This paper addresses the robust input-output energy decoupling problem for uncertain singular systems in which all parameter matrices except E exist as time-varying uncertainties. By means of linear matrix inequalities (LMIs), sufficient conditions are derived for the existence of linear state feedback and input transformation control laws, such that the resulting closed-loop uncertain singular system is generalized quadratically stable and the energy of every input controls mainly the energy of a corresponding output, and influences the energy of other outputs as weakly as possible. Keywords Uncertain singular systems - generalized quadratical stability - input-output energy decoupling - linear matrix inequality (LMI) Xin-Zhuang Dong graduated from the Institute of Information Engineering of People’s Liberation Army, China, in 1994. She received the M. S. degree from the Institute of Electronic Technology of People’s Liberation Army, in 1998 and the Ph.D. degree from Northeastern University, China, in 2004. She is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, CAS.Her research interests include singular and nonlinear systems, especially the control of singular systems such as H ∞ control, passive control and dissipative control. Qing-Ling Zhang received the Ph.D. degree from Northeastern University, China, in 1995. He is currently a professor with the Institute of Systems Science, Northeastern University. His research interests include singular systems, fuzzy systems, decentralized control, and H 2/H ∞ control.

Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.

Robust Stabilization Analysis for Uncertain Systems with Time-Varying Delays

In this paper, the stabilization problem for uncertain systems with time-varying delays both in state and control are discussed. A stabilization criterion is obtained to guarantee the quadratic stability of the closed-loop system. The controller gain matrix is included in an Hamiltonian matrix, which is easily constructed by the boundedness of the uncertainties.

Fault-Tolerant Control for a Class of Uncertain Systems with Actuator Faults

The problem of fault-tolerant controller design for a class of polytopic uncertain systems with actuator faults is studied in this paper. The actuator faults are presented as a more general and practical continuous fault model. Based on the affine quadratic stability （AQS）, the stability of the polytopic uncertain system is replaced by the stability at all corners of the polytope. For a wide range of problems including H∞ and mixed H2/H∞ controller design, sufficient conditions are derived to guarantee the robust stability and performance of the closed-loop system in both normal and fault cases. In the framework of the linear matrix inequality （LMI） method, an iterative algorithm is developed to reduce conservativeness of the design procedure. The effectiveness of the proposed design is shown through a flight control example.

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law.The results of this paper are also applied to switched linear systems.

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities （LMIs）, then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.