The paper presents a method of determining of the Lyapunov quadratic functional for linear time-invariant system with two delays both retarded and neutral type. The Lyapunov functional is constructed for a given its time derivative which is calculated on the trajectory of the system with two delays both retarded and neutral type. The presented method gives analytical formulas for the coefficien...

In this paper we show some symmetry properties of Lyapunov exponents of a dynamical system when the linearized problem evolves on a quadratic group, X HX = H , with H orthogonal. It is well understood that in this case the exponents are symmetric with respect to the origin. Here, we give lower bounds on the number of Lyapunov exponents which are 0, and show that some Lyapunov exponents may have...

This paper considers the dynamic output feedback controller design problem for decentralized GCS(guaranteed cost stabilization) of large-scale systems with time delays in subsystem interconnections and nonlinear uncertainties. Based on the Lyapunov method, an LMI (linear matrix inequality) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability...

We address the safety-critical control problem for systems whose dynamics evolve on manifolds using the concepts of control Lyapunov functions (CLFs) and control Barrier functions (CBFs). We first extend the concepts of CLFs and CBFs from Cartesian spaces to manifolds, resulting in geometric CLFs and CBFs. We then formulate a state-dependent online quadratic program (QP) that imposes the constr...

This paper considers a quadratic stabilization problem by an H1 controller. The controller is constructed by a linear fractional transformation on contractive time-varying gains. The controller parameterization is given in terms of contractive time-varying gains. This free parameter can be used to improve the closed-loop response. A tuning method of time-varying gains is chosen so that a Lyapun...

This paper considers the dynamic output feedback controller design problem for decentralized guaranteed cost stabilization (GCS) of large-scale systems with time delays in subsystem interconnections. Based on the Lyapunov method, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bou...

In this paper, we propose a design method for guaranteed cost controllers for uncertain large-scale systems with time-delays in subsystem interconnections using delayed feedback. Based on the Lyapunov method, an LMI (Linear Matrix Inequality) optimization problem is formulated to design the delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numeric...

ABSTRACT. In this paper, we design a novel impulsive control law to stabilize a new class of chaotic systems. Using a non-quadratic Lyapunov function candidate and a stability theorem in [10], we derive some algebraic sufficient conditions which ensure the asymptotical stability of the chaotic system under the impulsive control strategy. Finally, a numerical example is presented to illustrate t...

In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model to compare with the conventional model based on the quadratic Lyapunov functional to be minimized during the retrieval process. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may b...