Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation...
This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility...
To tackle the underactuated surface vessel (USV) trajectory tracking challenge with input delays and composite disturbances, an integral time-delay sliding mode controller based on backstepping is discussed. First, the law of virtual velocity control is established by coordinate transformation and the position error is caused to converge utilizing the performance function. At the same time, based on the estimation of velocity vector by the high-gain observer (HGO), radial basis function (RBF) neural...
We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...
A pullback incremental attraction, a nonautonomous version of incremental stability, is introduced for nonautonomous systems that may have unbounded limiting solutions. Its characterisation by a Lyapunov function is indicated.