Linear quadratic regulator (LQR) with trajectory sensitivity minimization and structurally constrained controller was formulated in [2] and [4]. In these works, a gradient search method, which is a particular type of nonlinear programming, was used to solve the problem. In this paper, we propose a linear matrix inequality (LMI)-based method for the problem. This LMI is formulated with block-dia...

The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov-Krasovskii approach. In the networked control systems domain a similar delay stability problem is treated using a switched system transformation approach. The paper aims to establish a relation between the switched system transformation approac...

This paper deals with the stabilization of Takagi-Sugeno models (T-S) using state feedback controllers. New sufficient stability conditions are given for both continuous and discrete T-S models. The stability conditions, formulated in term of bilinear matrix inequalities (BMIs), are based on a piecewise quadratic Lyapunov function and the use of the so-called S-procedure. A method of linearisat...

This paper focuses on the problems of a diagonal common quadratic Lyapunov function (DCQLF) existence for sets of stable positive linear time-invariant (LTI) systems. We derive the equivalent algebraic conditions to verify the existence of a DCQLF, namely that the finite number Hurwitz Mezler matrices at least have a common diagonal Stein solution. Finally some reduced cases are considered. 201...

This paper proposes an adaptive control for the nonlinear boost inverter with nonresistive load in order to cope with unknown resistive load as well as unknown inductive load. The adaptive control is accomplished by using a state observer to one side of the inverter with a quadratic Lyapunov function and by measuring the states variables. The stability of the complete system is analyzed by mean...

The target of this paper is to draw attention to some important relations between different procedures of state space synthesis of discrete linear systems optimizing the quadratic cost function. Common form of the synthesis concerns one-dimensional and multi-dimensional control problems solved by Second Method of Lyapunov, Maximum Principle of Pontryagin and by Bellamn's Dynamic Programming. Em...

The original version of this paper appeared in Linear Algebra and its Applications, volume 430, pp.34 40, 2009. Here we correct a slight gap in the statement and proof of Lemma 3.1 in that paper. We revisit the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system [1]. We use recently derived r...

This paper presents an approach to apply L1 adaptive control for output regulation in the presence of nonlinear uncertainty in underactuated hybrid systems with application to bipedal walking. The reference model is generated by control Lyapunov function based quadratic program (CLFQP) controller and is nonlinear. We evaluate our proposed control design on a model of RABBIT, a five-link planar ...

Abstract: This paper considers local stability analysis of discrete-time Takagi-Sugeno fuzzy systems, for which classically in the TS literature only global stability is considered. Using a common quadratic and nonquadratic Lyapunov function, respectively, LMI conditions are developed to establish local stability of an equilibrium point. An estimate of the region of attraction of this point is ...